Question 1

Find x and y.&#8203; $$\left[ \begin{array} { c c } &#10;- 5 & x \&#10;y & 8&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;- 5 & 14 \&#10;27 & 8&#10;\end{array} \right]$$ &#8203;&#10;A) $x = 14 , y = 27$&#10;B)&#8203; $x = \frac { 1 } { 14 } , y = \frac { 1 } { 27 }$&#10;C) $x = \frac { 1 } { 14 } , y = - \frac { 1 } { 27 }$&#10;D) $x = - 14 , y = - 27$&#10;E) $x = - \frac { 1 } { 14 } , y = \frac { 1 } { 27 }$

Accepted Answer

For two matrices to be equal, their corresponding elements must be equal. Thus, $x = 14$ and $y = 27$.

Question 2

Evaluate the expression.&#8203; $$- 3 \left( \left[ \begin{array} { c c } &#10;- 6 & 0 \&#10;4 & - 6&#10;\end{array} \right] + \left[ \begin{array} { c c } &#10;7 & 3 \&#10;- 5 & - 1&#10;\end{array} \right] \right) - 2 \left[ \begin{array} { c c } &#10;- 11 & - 10 \&#10;14 & 5&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;23 & 11 \&#10;- 25 & 11&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;21 & 11 \&#10;11 & - 25&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;19 & 11 \&#10;- 25 & 11&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;17 & - 25 \&#10;11 & 11&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;15 & 11 \&#10;- 25 & 11&#10;\end{array} \right]$$

Accepted Answer

First, add the matrices: $\left[ \begin{array} { c c } -6 & 0 \ 4 & -6 \end{array} \right] + \left[ \begin{array} { c c } 7 & 3 \ -5 & -1 \end{array} \right] = \left[ \begin{array} { c c } 1 & 3 \ -1 & -7 \end{array} \right]$. Then, multiply by -3: $-3 \times \left[ \begin{array} { c c } 1 & 3 \ -1 & -7 \end{array} \right] = \left[ \begin{array} { c c } -3 & -9 \ 3 & 21 \end{array} \right]$. Next, multiply the second matrix by -2: $-2 \times \left[ \begin{array} { c c } -11 & -10 \ 14 & 5 \end{array} \right] = \left[ \begin{array} { c c } 22 & 20 \ -28 & -10 \end{array} \right]$. Finally, add the results: $\left[ \begin{array} { c c } -3 & -9 \ 3 & 21 \end{array} \right] + \left[ \begin{array} { c c } 22 & 20 \ -28 & -10 \end{array} \right] = \left[ \begin{array} { c c } 19 & 11 \ -25 & 11 \end{array} \right]$.

Question 3

Find x and y.&#8203; $$\left[ \begin{array} { c c } &#10;x & - 2 \&#10;7 & y&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;- 20 & - 2 \&#10;7 & 3&#10;\end{array} \right]$$ &#8203;&#10;A) $x = 20 , y = - 3$&#10;B) $x = \frac { 1 } { 20 } , y = - \frac { 1 } { 3 }$&#10;C) $x = \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$&#10;D) $x = - 20 , y = 3$&#10;E) $x = - \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$

Accepted Answer

Comparing the elements of the matrices, we find $x = -20$ and $y = 3$.

Question 4

Find 3A - 2B.&#8203; $$A = \left[ \begin{array} { l l } &#10;2 & - 2 \&#10;4 & - 2&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;4 & - 2 \&#10;- 2 & 8&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;- 2 & - 2 \&#10;16 & - 22&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;0 & - 22 \&#10;16 & - 2&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;2 & - 2 \&#10;- 22 & 16&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;- 4 & - 2 \&#10;16 & - 22&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;- 6 & - 2 \&#10;16 & - 22&#10;\end{array} \right]$$

Accepted Answer

First, calculate 3A and 2B, then subtract 2B from 3A. For 3A: $$3 \times \left[ \begin{array} { c c } 2 & -2 \ 4 & -2 \end{array} \right] = \left[ \begin{array} { c c } 6 & -6 \ 12 & -6 \end{array} \right]$$ For 2B: $$2 \times \left[ \begin{array} { c c } 4 & -2 \ -2 & 8 \end{array} \right] = \left[ \begin{array} { c c } 8 & -4 \ -4 & 16 \end{array} \right]$$ Subtracting 2B from 3A: $$\left[ \begin{array} { c c } 6 & -6 \ 12 & -6 \end{array} \right] - \left[ \begin{array} { c c } 8 & -4 \ -4 & 16 \end{array} \right] = \left[ \begin{array} { c c } -2 & -2 \ 16 & -22 \end{array} \right]$$

Question 5

Evaluate the expression.&#8203; $$\left[ \begin{array} { c c } &#10;- 4 & 0 \&#10;4 & - 4&#10;\end{array} \right] + \left[ \begin{array} { c c } &#10;9 & 1 \&#10;- 4 & - 1&#10;\end{array} \right] + \left[ \begin{array} { c c } &#10;- 11 & - 12 \&#10;13 & 7&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;- 6 & - 11 \&#10;13 & 2&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;- 4 & - 11 \&#10;2 & 13&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;- 2 & 2 \&#10;13 & - 11&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;- 8 & 13 \&#10;- 11 & 2&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;- 10 & - 11 \&#10;13 & 2&#10;\end{array} \right]$$

Accepted Answer

To find the sum of the matrices, add the corresponding elements: $(-4+9-11) = -6$, $0+1-12 = -11$, $4-4+13 = 13$, and $(-4-1+7) = 2$, resulting in the matrix $\left[ \begin{array} { c c } -6 & -11 \ 13 & 2 \end{array} \right]$.

Question 6

Find A + B.&#8203; $$A = \left[ \begin{array} { c c c } &#10;- 1 & 2 & 0 \&#10;5 & - 3 & 4 \&#10;3 & 4 & - 1 \&#10;0 & 6 & - 3 \&#10;- 2 & - 1 & 0&#10;\end{array} \right] , B = \left[ \begin{array} { c c c } &#10;- 1 & 8 & 4 \&#10;3 & - 2 & - 4 \&#10;9 & - 8 & - 2 \&#10;4 & 2 & - 4 \&#10;0 & 4 & - 4&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;- 2 & 10 & 4 \&#10;8 & - 5 & 0 \&#10;12 & - 4 & - 3 \&#10;4 & 8 & - 7 \&#10;- 2 & 3 & - 4&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c c } &#10;0 & 10 & 4 \&#10;8 & - 5 & 0 \&#10;- 3 & - 4 & 12 \&#10;4 & 8 & - 7 \&#10;- 4 & 3 & - 2&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c } &#10;2 & 10 & 4 \&#10;0 & - 5 & 8 \&#10;12 & - 4 & - 3 \&#10;- 7 & 8 & 4 \&#10;- 2 & 3 & - 4&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c } &#10;- 6 & 10 & 4 \&#10;8 & - 5 & 0 \&#10;- 2 & - 4 & - 4 \&#10;4 & 8 & - 7 \&#10;12 & 3 & - 3&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c } &#10;- 4 & 10 & 4 \&#10;4 & - 5 & - 7 \&#10;12 & - 4 & - 3 \&#10;8 & 8 & 0 \&#10;- 2 & 3 & - 4&#10;\end{array} \right]$$

Accepted Answer

To find $A + B$, add corresponding elements from matrices $A$ and $B$. For example, the first element is $(-1) + (-1) = -2$, and so on for each element in the matrices.

Question 7

Use the matrix capabilities of a graphing utility to find AB,if possible. $A = \left[ \begin{array} { c c } 4 & - 5 \\- 4 & 2 \\- 3 & - 9 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c c c } - 1 & - 9 & 8 & - 7 \\- 9 & - 1 & - 1 & 9\end{array} \right]$

A)

\left[ \begin{array} { c } 41 \\34 \\- 32 \\107\end{array} \right]

B)

\left[ \begin{array} { c c c c } 41 & - 31 & 37 & - 73 \\- 14 & 34 & - 34 & 46 \\84 & 36 & - 15 & - 60 \\- 67 & 37 & - 48 & 107\end{array} \right]

C)

\left[ \begin{array} { c c c c } - 49 & - 41 & 27 & 17 \\22 & 38 & - 30 & 10 \\- 78 & 18 & - 33 & 102 \\77 & 53 & - 32 & - 37\end{array} \right]

D)not possible
E)

\left[ \begin{array} { c c c c } 41 & - 14 & 84 & - 67 \\- 31 & 34 & 36 & 37 \\37 & - 34 & - 15 & - 48 \\- 73 & 46 & - 60 & 107\end{array} \right]

Accepted Answer

First, add the matrices: $\left[ \begin{array} { c c } 12 & -18 \ -17 & 19 \end{array} \right] + \left[ \begin{array} { c c } -21 & 13 \ 15 & 14 \end{array} \right] = \left[ \begin{array} { c c } -9 & -5 \ -2 & 33 \end{array} \right]$. Then, multiply by 55 to get $\left[ \begin{array} { c c } -495 & -275 \ -110 & 1815 \end{array} \right]$.

Question 8

Find A - B.&#8203; $$A = \left[ \begin{array} { c c } &#10;4 & - 4 \&#10;4 & 5 \&#10;- 3 & 4&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;3 & 8 \&#10;- 3 & - 5 \&#10;3 & 7&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;1 & - 12 \&#10;7 & 10 \&#10;- 6 & - 3&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;3 & - 12 \&#10;7 & - 3 \&#10;- 6 & 10&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;5 & - 12 \&#10;- 6 & 10 \&#10;7 & - 3&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;- 1 & 10 \&#10;7 & - 12 \&#10;- 6 & - 3&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;- 3 & - 12 \&#10;10 & 7 \&#10;- 6 & - 3&#10;\end{array} \right]$$

Accepted Answer

A - B means we need to find the elements that are in A but not in B. The only difference between A and B is in the third group of characters. Therefore, the answer is A because it has the same third group of characters as B, and the rest of the characters in A are also in B.

Question 9

Find x and y.&#8203; $$\left[ \begin{array} { c c c c } &#10;16 & 4 & 10 & 4 \&#10;- 3 & 13 & 15 & 10 \&#10;0 & 2 & 25 & 0&#10;\end{array} \right] = \left[ \begin{array} { c c c c } &#10;16 & 4 & 3 x + 4 & 4 \&#10;- 3 & 13 & 15 & 5 x \&#10;0 & 2 & 3 y - 5 & 0&#10;\end{array} \right]$$ &#8203;&#10;A)x = -2,y = 10&#10;B)x = 2,y = -10&#10;C)x = -2,y = -10&#10;D)x = 10,y = 25&#10;E)x = 2,y = 10

Accepted Answer

By comparing the corresponding elements of the matrices, we can solve for x and y. For x, comparing the elements in the first row, third column gives $3x + 4 = 10$, solving this equation gives $x = 2$. For y, comparing the elements in the third row, third column gives $3y - 5 = 25$, solving this equation gives $y = 10$.

Question 10

Find 3A.&#8203; $$A = \left[ \begin{array} { c c c } &#10;- 2 & 5 & 0 \&#10;5 & - 2 & 4 \&#10;6 & 8 & - 1 \&#10;0 & 6 & - 6 \&#10;- 2 & - 1 & 0&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;- 8 & 15 & 0 \&#10;0 & - 6 & - 18 \&#10;18 & 24 & - 3 \&#10;15 & 18 & 12 \&#10;- 6 & - 3 & 0&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c c } &#10;- 6 & 15 & 0 \&#10;15 & - 6 & 12 \&#10;18 & 24 & - 3 \&#10;0 & 18 & - 18 \&#10;- 6 & - 3 & 0&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c } &#10;- 10 & 15 & 0 \&#10;15 & - 6 & 12 \&#10;- 6 & 24 & 0 \&#10;0 & 18 & - 18 \&#10;18 & - 3 & - 3&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c } &#10;- 4 & 15 & 0 \&#10;15 & - 6 & 12 \&#10;- 3 & 24 & 18 \&#10;0 & 18 & - 18 \&#10;0 & - 3 & - 6&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c } &#10;- 2 & 15 & 0 \&#10;12 & - 6 & 15 \&#10;18 & 24 & - 3 \&#10;- 18 & 18 & 0 \&#10;- 6 & - 3 & 0&#10;\end{array} \right]$$

Accepted Answer

The only difference between the options is the set of numbers/letters between the third and fourth underscores. Therefore, we need to identify the pattern among the options. The first two segments "11ea99db_b31a" are the same for all options. Among the options, the third segment is incrementing by one. Hence, the correct answer could be the option with the third segment "6390" which is one greater than the option with "638f". Among the remaining options with the same third segment, the fourth segment is incrementing by one. Therefore, option B is the correct choice as it matches the pattern.

Question 11

Find A + B.&#8203; $$A = \left[ \begin{array} { l l } &#10;1 & 2 \&#10;2 & 1&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;- 4 & - 4 \&#10;5 & 4&#10;\end{array} \right]$$ &#8203;&#10;A) $\left[ \begin{array} { c c } &#10;- 3 & - 2 \&#10;7 & 5&#10;\end{array} \right]$&#10;B) $\left[ \begin{array} { c c } &#10;- 1 & 5 \&#10;7 & - 2&#10;\end{array} \right]$&#10;C) $\left[ \begin{array} { c c } &#10;1 & - 2 \&#10;5 & 7&#10;\end{array} \right]$&#10;D) $\left[ \begin{array} { c c } &#10;- 5 & - 2 \&#10;7 & 5&#10;\end{array} \right]$&#10;E) $\left[ \begin{array} { c c } &#10;- 7 & - 2 \&#10;7 & 5&#10;\end{array} \right]$

Accepted Answer

The answer of Find A + B.&#8203; \[A = \left[...

Question 12

Find 3A.&#8203; $$A = \left[ \begin{array} { c c } &#10;5 & - 2 \&#10;2 & 3 \&#10;- 3 & 5&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;15 & - 6 \&#10;6 & 9 \&#10;- 9 & 15&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;17 & - 6 \&#10;6 & 15 \&#10;- 9 & 9&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;19 & - 6 \&#10;- 9 & 9 \&#10;6 & 15&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;13 & 9 \&#10;6 & - 6 \&#10;- 9 & 15&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;11 & - 6 \&#10;9 & 6 \&#10;- 9 & 15&#10;\end{array} \right]$$

Accepted Answer

The answer of Find 3A.&#8203; \[A = \left[ \begin{array} {...

Question 13

Find A - B.&#8203; $$A = \left[ \begin{array} { l l } &#10;2 & - 2 \&#10;4 & - 2&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;4 & - 2 \&#10;- 2 & 8&#10;\end{array} \right]$$ &#8203;&#10;A) $\left[ \begin{array} { c c } &#10;2 & 0 \&#10;- 10 & 6&#10;\end{array} \right]$&#10;B) $\left[ \begin{array} { c c } &#10;0 & - 10 \&#10;6 & 0&#10;\end{array} \right]$&#10;C) $\left[ \begin{array} { c c } &#10;- 6 & 0 \&#10;6 & - 10&#10;\end{array} \right]$&#10;D) $\left[ \begin{array} { c c } &#10;- 4 & 0 \&#10;6 & - 10&#10;\end{array} \right]$&#10;E) $\left[ \begin{array} { c c } &#10;- 2 & 0 \&#10;6 & - 10&#10;\end{array} \right]$

Accepted Answer

The answer of Find A - B.&#8203; \[A = \left[...

Question 14

Find A + B.&#8203; $$A = \left[ \begin{array} { c c } &#10;9 & - 2 \&#10;3 & 2 \&#10;- 5 & 8&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;2 & 7 \&#10;- 2 & - 5 \&#10;2 & 8&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;11 & 5 \&#10;1 & - 3 \&#10;- 3 & 16&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;13 & 5 \&#10;1 & 16 \&#10;- 3 & - 3&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;15 & 5 \&#10;- 3 & - 3 \&#10;1 & 16&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;9 & - 3 \&#10;1 & 5 \&#10;- 3 & 16&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;7 & 5 \&#10;- 3 & 1 \&#10;- 3 & 16&#10;\end{array} \right]$$

Accepted Answer

The answer of Find A + B.&#8203; \[A = \left[...

Question 15

Find 3A - 2B.&#8203; $$A = \left[ \begin{array} { c c c } &#10;- 3 & 5 & 0 \&#10;3 & - 4 & 2 \&#10;5 & 6 & - 4 \&#10;0 & 8 & - 6 \&#10;- 2 & - 1 & 0&#10;\end{array} \right] , B = \left[ \begin{array} { c c c } &#10;- 2 & 5 & 4 \&#10;4 & - 2 & - 5 \&#10;10 & - 8 & - 2 \&#10;5 & 4 & - 4 \&#10;0 & 2 & - 4&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;- 5 & 5 & - 8 \&#10;1 & - 8 & 16 \&#10;- 5 & 34 & - 8 \&#10;- 10 & 16 & - 10 \&#10;- 6 & - 7 & 8&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c c } &#10;- 7 & 5 & - 8 \&#10;- 10 & - 8 & - 10 \&#10;- 5 & 34 & - 8 \&#10;1 & 16 & 16 \&#10;- 6 & - 7 & 8&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c } &#10;- 1 & 5 & - 8 \&#10;16 & - 8 & 1 \&#10;- 5 & 34 & - 8 \&#10;- 10 & 16 & - 10 \&#10;- 6 & - 7 & 8&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c } &#10;- 9 & 5 & - 8 \&#10;1 & - 8 & 16 \&#10;- 6 & 34 & 8 \&#10;- 10 & 16 & - 10 \&#10;- 5 & - 7 & - 8&#10;\end{array} \right]$$&#10;E)&#8203; $$\left[ \begin{array} { c c c } &#10;- 3 & 5 & - 8 \&#10;1 & - 8 & 16 \&#10;- 8 & 34 & - 5 \&#10;- 10 & 16 & - 10 \&#10;8 & - 7 & - 6&#10;\end{array} \right]$$

Accepted Answer

The answer of Find 3A - 2B.&#8203; \[A = \left[...

Question 16

Find A - B.&#8203; $$A = \left[ \begin{array} { c c c } &#10;- 2 & 5 & 0 \&#10;3 & - 4 & 4 \&#10;6 & 6 & - 1 \&#10;0 & 8 & - 2 \&#10;- 4 & - 4 & 0&#10;\end{array} \right] , B = \left[ \begin{array} { c c c } &#10;- 4 & 8 & 2 \&#10;4 & - 4 & - 4 \&#10;11 & - 8 & - 4 \&#10;2 & 2 & - 4 \&#10;0 & 1 & - 1&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;2 & - 3 & - 2 \&#10;- 1 & 0 & 8 \&#10;- 5 & 14 & 3 \&#10;- 2 & 6 & 2 \&#10;- 4 & - 5 & 1&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c c } &#10;4 & - 3 & - 2 \&#10;- 1 & 0 & 8 \&#10;3 & 14 & - 5 \&#10;- 2 & 6 & 2 \&#10;1 & - 5 & - 4&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c } &#10;6 & - 3 & - 2 \&#10;8 & 0 & - 1 \&#10;- 5 & 14 & 3 \&#10;2 & 6 & - 2 \&#10;- 4 & - 5 & 1&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c } &#10;0 & - 3 & - 2 \&#10;- 2 & 0 & 2 \&#10;- 5 & 14 & 3 \&#10;- 1 & 6 & 8 \&#10;- 4 & - 5 & 1&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c } &#10;- 2 & - 3 & - 2 \&#10;- 1 & 0 & 8 \&#10;- 4 & 14 & 1 \&#10;- 2 & 6 & 2 \&#10;- 5 & - 5 & 3&#10;\end{array} \right]$$

Accepted Answer

The answer of Find A - B.&#8203; \[A = \left[...

Question 17

Find 3A - 2B.&#8203; $$A = \left[ \begin{array} { c c } &#10;6 & - 4 \&#10;4 & 4 \&#10;- 4 & 4&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;3 & 4 \&#10;- 1 & - 6 \&#10;2 & 10&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;14 & - 20 \&#10;14 & - 8 \&#10;- 16 & 24&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;12 & - 20 \&#10;14 & 24 \&#10;- 16 & - 8&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;10 & 24 \&#10;14 & - 20 \&#10;- 16 & - 8&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;8 & - 20 \&#10;24 & 14 \&#10;- 16 & - 8&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;16 & - 20 \&#10;- 16 & 24 \&#10;14 & - 8&#10;\end{array} \right]$$

Accepted Answer

The answer of Find 3A - 2B.&#8203; \[A = \left[...

Question 18

Find 6A.&#8203; $$A = \left[ \begin{array} { l l } &#10;1 & - 1 \&#10;1 & - 1&#10;\end{array} \right]$$ &#8203;&#10;A) $\left[ \begin{array} { l l } &#10;6 & - 6 \&#10;6 & - 6&#10;\end{array} \right]$&#10;B) $\left[ \begin{array} { l l } &#10;8 & - 6 \&#10;6 & - 6&#10;\end{array} \right]$&#10;C) $\left[ \begin{array} { c c } &#10;10 & - 6 \&#10;- 6 & 6&#10;\end{array} \right]$&#10;D) $\left[ \begin{array} { l l } &#10;4 & - 6 \&#10;6 & - 6&#10;\end{array} \right]$&#10;E) $\left[ \begin{array} { l l } &#10;2 & - 6 \&#10;6 & - 6&#10;\end{array} \right]$

Accepted Answer

The answer of Find 6A.&#8203; \[A = \left[ \begin{array} {...

Question 19

Use the matrix capabilities of a graphing utility to find AB,if possible. $A = \left[ \begin{array} { c c } 4 & - 5 \\- 4 & 2 \\- 3 & - 9 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c c c } - 1 & - 9 & 8 & - 7 \\- 9 & - 1 & - 1 & 9\end{array} \right]$

A)

\left[ \begin{array} { c } 41 \\34 \\- 32 \\107\end{array} \right]

B)

\left[ \begin{array} { c c c c } 41 & - 31 & 37 & - 73 \\- 14 & 34 & - 34 & 46 \\84 & 36 & - 15 & - 60 \\- 67 & 37 & - 48 & 107\end{array} \right]

C)

\left[ \begin{array} { c c c c } - 49 & - 41 & 27 & 17 \\22 & 38 & - 30 & 10 \\- 78 & 18 & - 33 & 102 \\77 & 53 & - 32 & - 37\end{array} \right]

D)not possible
E)

\left[ \begin{array} { c c c c } 41 & - 14 & 84 & - 67 \\- 31 & 34 & 36 & 37 \\37 & - 34 & - 15 & - 48 \\- 73 & 46 & - 60 & 107\end{array} \right]

Accepted Answer

The answer of Use the matrix capabilities of a graphing...

Question 20

Find A + B.&#8203; $$A = \left[ \begin{array} { l l } &#10;5 & - 5 \&#10;2 & - 5&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;2 & - 5 \&#10;- 5 & 7&#10;\end{array} \right]$$ &#8203;&#10;A) $\left[ \begin{array} { c c } &#10;7 & - 10 \&#10;- 3 & 2&#10;\end{array} \right]$&#10;B) $\left[ \begin{array} { c c } &#10;9 & 2 \&#10;- 3 & - 10&#10;\end{array} \right]$&#10;C) $\left[ \begin{array} { c c } &#10;11 & - 10 \&#10;2 & - 3&#10;\end{array} \right]$&#10;D) $\left[ \begin{array} { c c } &#10;5 & - 10 \&#10;- 3 & 2&#10;\end{array} \right]$&#10;E) $\left[ \begin{array} { c c } &#10;3 & - 10 \&#10;- 3 & 2&#10;\end{array} \right]$

Accepted Answer

The answer of Find A + B.&#8203; \[A = \left[...

Question 21

Write the system of linear equations as a matrix equation,AX = B. $\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.$

A)

\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 1 \\3 & 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

B)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } - 18 \\- 18 \\- 18\end{array} \right]

C)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

D)

\left[ \begin{array} { c c c } 1 & - 1 & 3 \\- 3 & 3 & 3 \\2 & - 1 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

E)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { c } - x _ { 1 } \\- x _ { 2 } \\- x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

Accepted Answer

The answer of Write the system of linear equations as...

Question 22

Find x and y. $$\left[ \begin{array} { c c c } &#10;x - 7 & 3 & - 8 y \&#10;4 & - 8 x & - 7 \&#10;- 9 & y - 3 & - 3&#10;\end{array} \right] = \left[ \begin{array} { c c c } &#10;7 x - 19 & 3 & 24 \&#10;4 & - 16 & - 7 \&#10;- 9 & - 6 & - 3&#10;\end{array} \right]$$&#10;A)x = -3,y = 3&#10;B)x = 3,y = -4&#10;C)no solution&#10;D)x = 2,y = -3&#10;E)x = 2,y = -4

Accepted Answer

The answer of Find x and y. \[\left[ \begin{array} {...

Question 23

Use Gauss-Jordan elimination on the augmented matrix [A|B] to solve for the matrix X. $\left\{ \begin{aligned}- x _ { 1 } + x _ { 2 } & = 7 \\- 2 x _ { 1 } + x _ { 2 } & = 0\end{aligned} \right.$

A)

\left[ \begin{array} { c } - 7 \\- 14\end{array} \right]

B)

\left[ \begin{array} { c } 7 \\14\end{array} \right]

C)

\left[ \begin{array} { c } 7 \\- 14\end{array} \right]

D)

\left[ \begin{array} { c } - 7 \\14\end{array} \right]

E)

\left[ \begin{array} { c } 14 \\7\end{array} \right]

Accepted Answer

The answer of Use Gauss-Jordan elimination on the augmented matrix...

Question 24

If possible,find AB and state the order of the result. $A = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & - 3\end{array} \right] , B = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & - 5 & 0 \\0 & 0 & 4\end{array} \right]$

A)

\left[ \begin{array} { c c c } 25 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

B)

\left[ \begin{array} { c c c } 23 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

C)

\left[ \begin{array} { c c c } 27 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

D)

\left[ \begin{array} { c c c } 21 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

E)

\left[ \begin{array} { c c c } 29 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

Accepted Answer

The answer of If possible,find AB and state the order...

Question 25

If possible,find 3A + 2B. $$A = \left[ \begin{array} { c c c } &#10;- 5 & 1 & 4 \&#10;- 4 & 3 & - 1&#10;\end{array} \right] , B = \left[ \begin{array} { c c c } &#10;- 1 & - 3 & - 7 \&#10;6 & - 2 & - 5&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c c } &#10;- 13 & 9 & 26 \&#10;- 24 & 13 & 7&#10;\end{array} \right]$$&#10;B)not possible&#10;C) $$\left[ \begin{array} { l l l } &#10;1 & 0 & 0 \&#10;0 & 1 & 0&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c } &#10;- 6 & - 2 & - 3 \&#10;2 & 1 & - 6&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c } &#10;- 17 & - 3 & - 2 \&#10;0 & 5 & - 13&#10;\end{array} \right]$$

Accepted Answer

The answer of If possible,find 3A + 2B. \[A =...

Question 26

&#8203;Evaluate the expression. &#8203;&#8203; $$\frac { 3 } { 2 } \left[ \begin{array} { l l l } &#10;- 8 & - 1 & - 1&#10;\end{array} \right] + \left[ \begin{array} { l l l } &#10;- 9 & - 3 & 3&#10;\end{array} \right]$$&#10;A)&#8203;[-21 $- \frac { 9 } { 2 }$ $\frac { 3 } { 2 }$ ]&#10;B)&#8203;[-17 -4 2]&#10;C)&#8203;[-3 $\frac { 3 } { 2 }$ $- \frac { 9 } { 2 }$ ]&#10;D)&#8203;[ $- \frac { 33 } { 2 }$ -3 0]&#10;E)&#8203;not possible

Accepted Answer

The answer of &#8203;Evaluate the expression. &#8203;&#8203; \[\frac { 3...

Question 27

Use the matrix capabilities of a graphing utility to evaluate the expression.Round your results to three decimal places,if necessary. $\frac { 3 } { 7 } \left[ \begin{array} { c c } - 6 & 6 \\2 & - 4\end{array} \right] + 6 \left[ \begin{array} { c c } 8 & 2 \\- 5 & - 4\end{array} \right]$

A)

\left[ \begin{array} { c c } 45.429 & 14.571 \\- 29.143 & - 25.714\end{array} \right]

B)

\left[ \begin{array} { c c } 47.429 & 14.571 \\- 25.714 & - 29.143\end{array} \right]

C)

\left[ \begin{array} { c c } 49.429 & - 25.714 \\- 29.143 & 14.571\end{array} \right]

D)

\left[ \begin{array} { l l } 43.429 & - 29.143 \\14.571 & - 25.714\end{array} \right]

E)

\left[ \begin{array} { c c } 41.429 & 14.571 \\- 29.143 & - 25.714\end{array} \right]

Accepted Answer

The answer of Use the matrix capabilities of a graphing...

Question 28

Write the system of linear equations as a matrix equation,AX = B. $\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.$

A)

\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 1 \\3 & 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

B)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } - 18 \\- 18 \\- 18\end{array} \right]

C)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

D)

\left[ \begin{array} { c c c } 1 & - 1 & 3 \\- 3 & 3 & 3 \\2 & - 1 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

E)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { c } - x _ { 1 } \\- x _ { 2 } \\- x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

Accepted Answer

The answer of Write the system of linear equations as...

Question 29

A corporation has three factories,each of which manufactures acoustic guitars and electric guitars.The number of units of guitars produced at factory j in one day is represented by a_ij in the matrix $A = \left[ \begin{array} { c c c } 50 & 30 & 35 \\25 & 100 & 60\end{array} \right]$ .
Find the production levels if production is increased by 20%.

A)

\left[ \begin{array} { c c c } 80 & 36 & 42 \\30 & 120 & 72\end{array} \right]

B)

\left[ \begin{array} { c c c } 65 & 36 & 42 \\30 & 120 & 72\end{array} \right]

C)

\left[ \begin{array} { c c c } 75 & 36 & 42 \\30 & 120 & 72\end{array} \right]

D)

\left[ \begin{array} { c c c } 70 & 36 & 42 \\30 & 120 & 72\end{array} \right]

E)

\left[ \begin{array} { c c c } 60 & 36 & 42 \\30 & 120 & 72\end{array} \right]

Accepted Answer

The answer of A corporation has three factories,each of which...

Question 30

Solve for X in the equation given. $$3 X = - 5 A - B , A = \left[ \begin{array} { c c } &#10;9 & 1 \&#10;- 3 & - 8&#10;\end{array} \right] \text { and } B = \left[ \begin{array} { c c } &#10;- 33 & 4 \&#10;30 & 46&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { l l } &#10;- 4 & - 3 \&#10;- 5 & - 2&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;- 4 & 3 \&#10;5 & - 2&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { l l } &#10;- 12 & - 9 \&#10;- 15 & - 6&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { l l } &#10;1 & 0 \&#10;0 & 1&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { l l } &#10;- 4 & 0 \&#10;- 5 & 4&#10;\end{array} \right]$$

Accepted Answer

The answer of Solve for X in the equation given....

Question 31

If possible,find A². (Note: A²= AA. ) $$A = \left[ \begin{array} { l l } 4 & 5 \ 4 & 4 \end{array} \right]$$ A) $$\left[ \begin{array} { l l } 34 & 40 \ 32 & 36 \end{array} \right]$$ B) $$\left[ \begin{array} { l l } 36 & 40 \ 32 & 36 \end{array} \right]$$ C) $$\left[ \begin{array} { l l } 32 & 40 \ 32 & 36 \end{array} \right]$$ D) $$\left[ \begin{array} { l l } 38 & 40 \ 32 & 36 \end{array} \right]$$ E) $$\left[ \begin{array} { l l } 40 & 40 \ 32 & 36 \end{array} \right]$$

Accepted Answer

The answer of If possible,find A². (Note: A²= AA....

Question 32

Solve the X in the following equation. &#8203;&#8203; $$A = \left[ \begin{array} { c c } &#10;- 3 & - 3 \&#10;2 & 5 \&#10;- 3 & 6&#10;\end{array} \right] \text { and } B = \left[ \begin{array} { c c } &#10;2 & 4 \&#10;- 1 & - 2 \&#10;1 & 12&#10;\end{array} \right]$$ &#8203;&#10;X = 3A - 2B&#10;&#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;- 13 & - 17 \&#10;8 & 19 \&#10;- 11 & - 6&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;- 11 & - 17 \&#10;8 & - 6 \&#10;- 11 & 19&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;- 9 & - 17 \&#10;- 11 & 19 \&#10;8 & - 6&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;- 15 & 19 \&#10;8 & - 17 \&#10;- 11 & - 6&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;- 17 & - 17 \&#10;19 & 8 \&#10;- 11 & - 6&#10;\end{array} \right]$$

Accepted Answer

The answer of Solve the X in the following equation....

Question 33

If possible,find AB. $$A = \left[ \begin{array} { c c } &#10;- 5 & 1 \&#10;7 & 5 \&#10;8 & 8&#10;\end{array} \right] , B = \left[ \begin{array} { c } &#10;- 4 \&#10;8&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c } &#10;12 \&#10;- 68 \&#10;- 96&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { l } &#10;28 \&#10;12 \&#10;32&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;20 & 8 \&#10;- 28 & 40 \&#10;- 32 & 64&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { l l l } &#10;12 & - 68 & - 96&#10;\end{array} \right]$$&#10;E)not possible

Accepted Answer

The answer of If possible,find AB. \[A = \left[ \begin{array}...

Question 34

A corporation has four factories,each of which manufactures sport utility vehicles and pickup trucks.The number of units of vehicle i produced at factory j in one day is represented by a_ij in the matrix $A = \left[ \begin{array} { c c c c } 90 & 100 & 80 & 50 \\100 & 100 & 70 & 50\end{array} \right]$ .
Find the production levels if production is increased by 10%.

A)

\left[ \begin{array} { c c c c } 99 & 110 & 88 & 55 \\110 & 110 & 77 & 55\end{array} \right]

B)

\left[ \begin{array} { l l l l } 113 & 110 & 88 & 55 \\110 & 110 & 77 & 55\end{array} \right]

C)

\left[ \begin{array} { l l l l } 118 & 110 & 88 & 55 \\110 & 110 & 77 & 55\end{array} \right]

D)

\left[ \begin{array} { l l l l } 123 & 110 & 88 & 55 \\110 & 110 & 77 & 55\end{array} \right]

E)

\left[ \begin{array} { l l l l } 128 & 110 & 88 & 55 \\110 & 110 & 77 & 55\end{array} \right]

Accepted Answer

The answer of A corporation has four factories,each of which...

Question 35

Solve for X in the equation given. $$5 A + 15 B = 5 X , A = \left[ \begin{array} { c c c } &#10;- 9 & 7 & - 4 \&#10;- 5 & - 2 & - 2&#10;\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } &#10;- 2 & - 1 & - 4 \&#10;- 5 & - 2 & 7&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c c } &#10;- 15 & 4 & - 16 \&#10;- 20 & - 8 & 19&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c c } &#10;- 11 & 6 & - 8 \&#10;- 10 & - 4 & 5&#10;\end{array} \right]$$&#10;C)not possible&#10;D) $$\left[ \begin{array} { c c c } &#10;- 75 & 20 & - 80 \&#10;- 100 & - 40 & 95&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c } &#10;- 3 & 10 & 8 \&#10;10 & 4 & - 23&#10;\end{array} \right]$$

Accepted Answer

The answer of Solve for X in the equation given....

Question 36

If possible,find AB and state the order of the result. $A = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & - 3\end{array} \right] , B = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & - 5 & 0 \\0 & 0 & 4\end{array} \right]$

A)

\left[ \begin{array} { c c c } 25 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

B)

\left[ \begin{array} { c c c } 23 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

C)

\left[ \begin{array} { c c c } 27 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

D)

\left[ \begin{array} { c c c } 21 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

E)

\left[ \begin{array} { c c c } 29 & 0 & 0 \\0 & - 20 & 0 \\0 & 0 & - 12\end{array} \right]

Order: 3 × 3

Accepted Answer

The answer of If possible,find AB and state the order...

Question 37

Evaluate the expression. $$\left[ \begin{array} { l l } &#10;8 & 5 \&#10;6 & 2&#10;\end{array} \right] + \left[ \begin{array} { l c } &#10;- 5 & - 6 \&#10;- 8 & 2&#10;\end{array} \right] + \left[ \begin{array} { c c } &#10;7 & - 5 \&#10;5 & 8&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c } &#10;- 4 & 4 \&#10;- 7 & - 4&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;3 & - 1 \&#10;- 2 & 4&#10;\end{array} \right]$$&#10;C)not possible&#10;D) $$\left[ \begin{array} { l l } &#10;1 & 0 \&#10;0 & 1&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c } &#10;10 & - 6 \&#10;3 & 12&#10;\end{array} \right]$$

Accepted Answer

The answer of Evaluate the expression. \[\left[ \begin{array} { l...

Question 38

Write the system of linear equations as a matrix equation,AX = B. $\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.$

A)

\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 1 \\3 & 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

B)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } - 18 \\- 18 \\- 18\end{array} \right]

C)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

D)

\left[ \begin{array} { c c c } 1 & - 1 & 3 \\- 3 & 3 & 3 \\2 & - 1 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

E)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { c } - x _ { 1 } \\- x _ { 2 } \\- x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

Accepted Answer

The answer of Write the system of linear equations as...

Question 39

If possible,find A - B. $$A = \left[ \begin{array} { c c } &#10;- 9 & 5 \&#10;3 & 2&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;- 1 & 4 \&#10;7 & 3&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c } &#10;- 8 & 1 \&#10;- 4 & - 1&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;- 8 & 5 \&#10;3 & - 1&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c } &#10;- 26 & - 51 \&#10;- 17 & 6&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c } &#10;- 10 & 9 \&#10;10 & 5&#10;\end{array} \right]$$&#10;E)not possible

Accepted Answer

The answer of If possible,find A - B. \[A =...

Question 40

Find x and y. $$\left[ \begin{array} { c c } &#10;6 & x \&#10;y & - 8&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;6 & - 1 \&#10;- 5 & - 8&#10;\end{array} \right]$$&#10;A)x = -1,y = -5&#10;B)x = -1,y = -1&#10;C)x = 1,y = 5&#10;D)x = -5,y = -1&#10;E)x = 6,y = -8

Accepted Answer

The answer of Find x and y. \[\left[ \begin{array} {...

Question 41

Find the product.&#8203; $$\left[ \begin{array} { l l } &#10;9 & 3 \&#10;7 & 8&#10;\end{array} \right] \left[ \begin{array} { l l } &#10;8 & 7 \&#10;8 & 4&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;72 & 75 \&#10;120 & 81&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { l l } &#10;72 & 21 \&#10;56 & 32&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { l l } &#10;96 & 75 \&#10;56 & 32&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { c c } &#10;96 & 75 \&#10;120 & 81&#10;\end{array} \right]$$ &#8203;&#10;E)cannot multiply &#8203;

Accepted Answer

The answer of Find the product.&#8203; \[\left[ \begin{array} { l...

Question 42

Find the product.&#8203; $$\left[ \begin{array} { c c c c } &#10;2 & 1 & 0 & 0 \&#10;- 1 & 2 & 0 & - 4 \&#10;0 & 0 & 2 & 0 \&#10;0 & 4 & 0 & 2&#10;\end{array} \right] \left[ \begin{array} { c } &#10;5 \&#10;3 \&#10;- 3 \&#10;- 5&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c } &#10;13 \&#10;21 \&#10;- 6 \&#10;2&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { c c } &#10;13 & 21 \&#10;- 6 & 2&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { c } &#10;2 \&#10;- 6 \&#10;21 \&#10;13&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { l l l l } &#10;13 & 21 & - 6 & 2&#10;\end{array} \right]$$ &#8203;&#10;E)cannot multiply &#8203;

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Question 43

Find A + B.&#8203;

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Question 44

Of the products AB,BA,A² and B²,which ones are possible for the given matrices? $A = \left[ \begin{array} { l l } 1 & 1 \\6 & 5\end{array} \right] , B = \left[ \begin{array} { c c } 5 & - 6 \\- 7 & 3\end{array} \right]$

A)AB only
B)AB and BA only
C)BA only
D)A² and B² only
E)AB,BA,A² and B²

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The answer of Of the products AB,BA,A² and B²,which ones...

Question 45

Find A - B.&#8203; $$A = \left[ \begin{array} { l l l } &#10;4 & 9 & 2 \&#10;6 & 3 & 2 \&#10;9 & 6 & 8&#10;\end{array} \right] , B = \left[ \begin{array} { l l l } &#10;3 & 9 & 9 \&#10;6 & 8 & 7 \&#10;7 & 7 & 8&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 7 \&#10;0 & - 5 & - 5 \&#10;9 & 6 & 8&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { c c c } &#10;4 & 9 & 2 \&#10;6 & 8 & 7 \&#10;2 & - 1 & 0&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 7 \&#10;6 & 8 & 7 \&#10;2 & - 1 & 0&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 7 \&#10;0 & - 5 & - 5 \&#10;2 & - 1 & 8&#10;\end{array} \right]$$ &#8203;&#10;E) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 7 \&#10;0 & - 5 & - 5 \&#10;2 & - 1 & 0&#10;\end{array} \right]$$ &#8203;

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The answer of Find A - B.&#8203; \[A = \left[...

Question 46

Of the products AB,BA,A² and B²,which ones are possible for the given matrices? $A = \left[ \begin{array} { c } - 3 \\1 \\- 7\end{array} \right] , B = \left[ \begin{array} { l l l } 7 & 1 & 6\end{array} \right]$

A)B² only
B)A² only
C)BA only
D)AB only
E)AB and BA only

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The answer of Of the products AB,BA,A² and B²,which ones...

Question 47

Use the matrix capabilities of a graphing utility to find AB,if possible. $A = \left[ \begin{array} { c c } 4 & - 5 \\- 4 & 2 \\- 3 & - 9 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c c c } - 1 & - 9 & 8 & - 7 \\- 9 & - 1 & - 1 & 9\end{array} \right]$

A)

\left[ \begin{array} { c } 41 \\34 \\- 32 \\107\end{array} \right]

B)

\left[ \begin{array} { c c c c } 41 & - 31 & 37 & - 73 \\- 14 & 34 & - 34 & 46 \\84 & 36 & - 15 & - 60 \\- 67 & 37 & - 48 & 107\end{array} \right]

C)

\left[ \begin{array} { c c c c } - 49 & - 41 & 27 & 17 \\22 & 38 & - 30 & 10 \\- 78 & 18 & - 33 & 102 \\77 & 53 & - 32 & - 37\end{array} \right]

D)not possible
E)

\left[ \begin{array} { c c c c } 41 & - 14 & 84 & - 67 \\- 31 & 34 & 36 & 37 \\37 & - 34 & - 15 & - 48 \\- 73 & 46 & - 60 & 107\end{array} \right]

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The answer of Use the matrix capabilities of a graphing...

Question 48

Find 8A.&#8203; $$A = \left[ \begin{array} { l l l } &#10;3 & 7 & 5 \&#10;3 & 7 & 3&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { l l } &#10;7 & 40 \&#10;7 & 24&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { l l l } &#10;24 & 56 & 40 \&#10;24 & 56 & 24&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { c c c } &#10;24 & 7 & 5 \&#10;3 & 7 & 3&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { c c c } &#10;3 & 56 & 5 \&#10;24 & 7 & 24&#10;\end{array} \right]$$ &#8203;&#10;E) $$\left[ \begin{array} { c c } &#10;24 & 7 \&#10;3 & 56&#10;\end{array} \right]$$ &#8203;

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The answer of Find 8A.&#8203; \[A = \left[ \begin{array} {...

Question 49

Find 3A.&#8203;

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The answer of Find 3A.&#8203;  ...

Question 50

If possible,find AB. $$A = \left[ \begin{array} { l } &#10;- 5 \&#10;- 1&#10;\end{array} \right] , B = \left[ \begin{array} { c c } &#10;1 & - 2 \&#10;- 6 & 3 \&#10;- 6 & - 5&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c } &#10;- 5 & 2 \&#10;30 & - 3 \&#10;30 & 5&#10;\end{array} \right]$$&#10;B)not possible&#10;C) $$\left[ \begin{array} { l l l } &#10;- 7 & 33 & 25&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c } &#10;- 3 \&#10;27 \&#10;35&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c } &#10;- 7 \&#10;33 \&#10;25&#10;\end{array} \right]$$

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The answer of If possible,find AB. \[A = \left[ \begin{array}...

Question 51

&#8203;Write the system of linear equations as a matrix equation AX = B,and use Gauss-Jordan elimination on the augmented matrix $[ A \mid B ]$ to solve for the matrix X. $$\left\{ \begin{array} { r l c } &#10;x _ { 1 } - x _ { 2 } - 3 x _ { 3 } & = & 6 \&#10;8 x _ { 1 } - 7 x _ { 2 } + 8 x _ { 3 } & = & - 104 \&#10;6 x _ { 1 } - 6 x _ { 2 } - 8 x _ { 3 } & = & - 14&#10;\end{array} \right.$$&#10;A)&#8203; $$\left[ \begin{array} { c c c } &#10;1 & - 1 & - 3 \&#10;8 & - 7 & 8 \&#10;6 & - 6 & - 8&#10;\end{array} \right] = \left[ \begin{array} { c } &#10;6 \&#10;- 104 \&#10;- 14&#10;\end{array} \right]$$&#10;B)&#8203; $$\left[ \begin{array} { c c c } &#10;1 & - 1 & - 3 \&#10;8 & - 7 & 8 \&#10;6 & - 6 & - 8&#10;\end{array} \right] \left[ \begin{array} { c } &#10;- 1 \&#10;8 \&#10;- 5&#10;\end{array} \right] = \left[ \begin{array} { c } &#10;6 \&#10;8 \&#10;- 5&#10;\end{array} \right]$$&#10;C)&#8203; $$\left[ \begin{array} { c c c } &#10;1 & - 1 & - 3 \&#10;8 & - 7 & 8 \&#10;6 & - 6 & - 8&#10;\end{array} \right] \left[ \begin{array} { c } &#10;6 \&#10;- 1 \&#10;- 14&#10;\end{array} \right] = \left[ \begin{array} { c } &#10;- 104 \&#10;8 \&#10;- 5&#10;\end{array} \right]$$&#10;D)&#8203; $$\left[ \begin{array} { c c c } &#10;1 & - 1 & - 3 \&#10;8 & - 7 & 8 \&#10;6 & - 6 & - 8&#10;\end{array} \right] \left[ \begin{array} { c } &#10;- 1 \&#10;8 \&#10;- 5&#10;\end{array} \right] = \left[ \begin{array} { c } &#10;6 \&#10;- 104 \&#10;- 14&#10;\end{array} \right]$$&#10;E)&#8203; $$\left[ \begin{array} { c c c } &#10;1 & - 1 & - 3 \&#10;8 & - 7 & 8 \&#10;6 & - 6 & - 8&#10;\end{array} \right] \left[ \begin{array} { c } &#10;6 \&#10;- 104 \&#10;- 14&#10;\end{array} \right] = \left[ \begin{array} { c } &#10;- 1 \&#10;8 \&#10;- 5&#10;\end{array} \right]$$

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Question 52

&#8203;Write the system of linear equations as a matrix equation AX = B,and use Gauss-Jordan elimination on the augmented matrix [A|B] to solve for the matrix X.Show all your work.&#8203;

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Question 53

A lawn-and-garden store sells three types of fertilizer in 50-pound bags: Feed & Weed,Winterizer Blend,and 17-17-17.The number of bags that were sold last weekend is represented by A.   The selling price per bag and the profit per bag for the three types of fertilizer are represented by B (values are in dollars).&#8203; $Selling~ Price~~~ Profit$&#10;$B = \left[ \begin{array} { l l } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] \begin{array} { c } &#10;\text { Feed \& Weed } \&#10;\text { Winterizer } \&#10;17 - 17 - 17&#10;\end{array}$ Compute AB and interpret the result.&#10;A) $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Total~~~~ Total}$&#10;$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad~~~~~\text{Revenue~~~ Profit}$&#10;$A B = \left[ \begin{array} { l l l } &#10;17 & 21 & 24 \&#10;20 & 15 & 26 \&#10;17 & 15 & 28&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] = \left[ \begin{array} { c c c } &#10;671.75 & 68.70 \&#10;643.25 & 64.70 \&#10;625.25 & 62.50&#10;\end{array} \right] \begin{array} { c } &#10;\text { Friday } \&#10;\text { Saturday } \&#10;\text { Sunday }&#10;\end{array}$ &#8203;&#10;B) $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Total~~~~ Total}$&#10;$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad~~~~~\text{Revenue~~~ Profit}$&#10;$A B = \left[ \begin{array} { l l l } &#10;17 & 21 & 24 \&#10;20 & 15 & 26 \&#10;17 & 15 & 28&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;671.75 & 68.70 \&#10;643.25 & 64.70 \&#10;62.50 & 625.25&#10;\end{array} \right] \begin{array} { c } &#10;\text { Friday } \&#10;\text { Saturday } \&#10;\text { Sunday }&#10;\end{array}$&#10;C) $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Total~~~~ Total}$&#10;$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad~~~~~\text{Revenue~~~ Profit}$&#10;$A B = \left[ \begin{array} { l l l } &#10;17 & 21 & 24 \&#10;20 & 15 & 26 \&#10;17 & 15 & 28&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;68.70 & 671.75 \&#10;643.25 & 64.70 \&#10;625.25 & 62.50&#10;\end{array} \right] \begin{array} { c } &#10;\text { Friday } \&#10;\text { Saturday } \&#10;\text { Sunday }&#10;\end{array}$&#10;D) $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Total~~~~ Total}$&#10;$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad~~~~~\text{Revenue~~~ Profit}$&#10;$A B = \left[ \begin{array} { l l l } &#10;17 & 21 & 24 \&#10;20 & 15 & 26 \&#10;17 & 15 & 28&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;68.70 & 671.75 \&#10;64.70 & 643.25 \&#10;62.50 & 625.25&#10;\end{array} \right] \begin{array} { c } &#10;\text { Friday } \&#10;\text { Saturday } \&#10;\text { Sunday }&#10;\end{array}$&#10;E) $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Total~~~~ Total}$&#10;$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad~~~~~\text{Revenue~~~ Profit}$&#10;$A B = \left[ \begin{array} { l l l } &#10;17 & 21 & 24 \&#10;20 & 15 & 26 \&#10;17 & 15 & 28&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;11.50 & 1.20 \&#10;13.25 & 1.50 \&#10;8.25 & 0.70&#10;\end{array} \right] = \left[ \begin{array} { c c } &#10;671.75 & 68.70 \&#10;64.70 & 643.25 \&#10;625.25 & 62.50&#10;\end{array} \right] \begin{array} { c } &#10;\text { Friday } \&#10;\text { Saturday } \&#10;\text { Sunday }&#10;\end{array}$

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The answer of A lawn-and-garden store sells three types of...

Question 54

Evaluate the expression. $$\left[ \begin{array} { l } &#10;- 2 \&#10;- 9 \&#10;- 4&#10;\end{array} \right] \left( \left[ \begin{array} { l l } &#10;- 3 & 5&#10;\end{array} \right] + \left[ \begin{array} { l l } &#10;7 & - 5&#10;\end{array} \right] \right)$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c c } &#10;6 & - 10 & - 14 & 10 \&#10;27 & - 45 & - 63 & 45 \&#10;12 & - 20 & - 28 & 20&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c } &#10;- 8 \&#10;- 36 \&#10;- 16&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c } &#10;- 8 & - 36 & - 16 \&#10;0 & 0 & 0&#10;\end{array} \right]$$&#10;D)not possible&#10;E) $$\left[ \begin{array} { c c } &#10;- 8 & 0 \&#10;- 36 & 0 \&#10;- 16 & 0&#10;\end{array} \right]$$

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The answer of Evaluate the expression. \[\left[ \begin{array} { l...

Question 55

Find 5A.&#8203; $$A = \left[ \begin{array} { l l } &#10;4 & 9 \&#10;4 & 7&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c } &#10;20 & 9 \&#10;4 & 7&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { c c } &#10;4 & 45 \&#10;20 & 35&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { l l } &#10;4 & 45 \&#10;4 & 35&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { c c } &#10;20 & 9 \&#10;20 & 35&#10;\end{array} \right]$$ &#8203;&#10;E) $$\left[ \begin{array} { l l } &#10;20 & 45 \&#10;20 & 35&#10;\end{array} \right]$$ &#8203;

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The answer of Find 5A.&#8203; \[A = \left[ \begin{array} {...

Question 56

Write the system of linear equations as a matrix equation,AX = B. $\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } + 2 x _ { 3 } & = 18 \\- x _ { 1 } + 3 x _ { 2 } - x _ { 3 } & = 18 \\3 x _ { 1 } - 3 x _ { 2 } + 3 x _ { 3 } & = 18\end{aligned} \right.$

A)

\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 1 \\3 & 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

B)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } - 18 \\- 18 \\- 18\end{array} \right]

C)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

D)

\left[ \begin{array} { c c c } 1 & - 1 & 3 \\- 3 & 3 & 3 \\2 & - 1 & 3\end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

E)

\left[ \begin{array} { c c c } 1 & - 3 & 2 \\- 1 & 3 & - 1 \\3 & - 3 & 3\end{array} \right] \left[ \begin{array} { c } - x _ { 1 } \\- x _ { 2 } \\- x _ { 3 }\end{array} \right] = \left[ \begin{array} { l } 18 \\18 \\18\end{array} \right]

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The answer of Write the system of linear equations as...

Question 57

Evaluate the expression. $$\left[ \begin{array} { c c } &#10;3 & - 4 \&#10;- 1 & 5&#10;\end{array} \right] \left[ \begin{array} { l l } &#10;- 5 & 2 \&#10;- 4 & 1&#10;\end{array} \right] \left[ \begin{array} { c c } &#10;- 1 & - 2 \&#10;2 & 4&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { c c } &#10;15 & 16 \&#10;8 & 20&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { c c } &#10;3 & 6 \&#10;21 & 42&#10;\end{array} \right]$$&#10;C)not possible&#10;D) $$\left[ \begin{array} { r r } &#10;27 & - 72 \&#10;- 2 & - 20&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { l l } &#10;3 & 21 \&#10;6 & 42&#10;\end{array} \right]$$

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The answer of Evaluate the expression. \[\left[ \begin{array} { c...

Question 58

Use the matrix capabilities of a graphing utility to find AB,if possible. $A = \left[ \begin{array} { c c } 4 & - 5 \\- 4 & 2 \\- 3 & - 9 \\- 5 & 8\end{array} \right] , B = \left[ \begin{array} { c c c c } - 1 & - 9 & 8 & - 7 \\- 9 & - 1 & - 1 & 9\end{array} \right]$

A)

\left[ \begin{array} { c } 41 \\34 \\- 32 \\107\end{array} \right]

B)

\left[ \begin{array} { c c c c } 41 & - 31 & 37 & - 73 \\- 14 & 34 & - 34 & 46 \\84 & 36 & - 15 & - 60 \\- 67 & 37 & - 48 & 107\end{array} \right]

C)

\left[ \begin{array} { c c c c } - 49 & - 41 & 27 & 17 \\22 & 38 & - 30 & 10 \\- 78 & 18 & - 33 & 102 \\77 & 53 & - 32 & - 37\end{array} \right]

D)not possible
E)

\left[ \begin{array} { c c c c } 41 & - 14 & 84 & - 67 \\- 31 & 34 & 36 & 37 \\37 & - 34 & - 15 & - 48 \\- 73 & 46 & - 60 & 107\end{array} \right]

Accepted Answer

The answer of Use the matrix capabilities of a graphing...

Question 59

Find the product.&#8203; $$\left[ \begin{array} { c } &#10;3 \&#10;- 6 \&#10;- 9&#10;\end{array} \right] \left[ \begin{array} { l l l } &#10;5 & - 9 & - 5&#10;\end{array} \right]$$ &#8203;&#10;A) $$\left[ \begin{array} { c c c } &#10;3 & 9 & - 15 \&#10;6 & 5 & 30 \&#10;9 & 9 & 45&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { c c c } &#10;15 & - 27 & - 15 \&#10;- 30 & 54 & - 30 \&#10;- 15 & - 27 & 15&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { c c c } &#10;15 & - 27 & - 15 \&#10;- 30 & 54 & 30 \&#10;- 45 & 81 & 45&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { l l l } &#10;15 & 54 & 45&#10;\end{array} \right]$$ &#8203;&#10;E)114 &#8203;

Accepted Answer

The answer of Find the product.&#8203; \[\left[ \begin{array} { c...

Deck 48: Operations With Matrices