Question 1

Select the order for the following matrix.&#8203; $$\left[ \begin{array} { l l l l } &#10;5 & - 4 & 3 & 3&#10;\end{array} \right]$$ &#8203;&#10;A)2 &#215; 2&#10;B)4 &#215; 4&#10;C)3 &#215; 1&#10;D)4 &#215; 1&#10;E)1 &#215; 4

Accepted Answer

The given matrix has 1 row and 4 columns, so its order is 1 × 4.

Question 2

Select the augmented matrix for the system of linear equations.&#8203; $$\left\{ \begin{aligned}&#10;x + 14 y - 12 z & = 12 \&#10;5 x - 4 y + 5 z & = 0 \&#10;12 x + y & = 9&#10;\end{aligned} \right.$$ &#8203;&#10;A)&#8203; $$\left[ \begin{array} { c c c c c } &#10;1 & 14 & 12 & \vdots & 12 \&#10;5 & - 4 & 5 & \vdots & 0 \&#10;12 & 1 & 0 & \vdots & 9&#10;\end{array} \right]$$&#10;B) $\left[\begin{array}{cccl}&#10;1 & 14 & -12 & :12 \&#10;5 & -4 & 5 & :0\&#10;12 & 1 & 0 & :9&#10;\end{array}\right]$&#10;C)&#8203; $\left[\begin{array}{cccl}&#10;1 & 14 & -12 & :12 \&#10;5 & 4 & 5 & :0\&#10;12 & 1 & 0 & :9&#10;\end{array}\right]$&#10;D)&#8203; $$\left[ \begin{array} { c c c c c } &#10;1 & 14 & 12 & \vdots & 12 \&#10;5 & 4 & 5 & \vdots & 0 \&#10;12 & 1 & 0 & \vdots & 9&#10;\end{array} \right]$$&#10;E)&#8203; $\left[\begin{array}{cccl}&#10;1 & 14 & -12 & :12 \&#10;5 & -4 & 5 & :0\&#10;12 & 1 & 9 & :0&#10;\end{array}\right]$

Accepted Answer

The correct augmented matrix must accurately represent the coefficients of $x$, $y$, and $z$ from the system of equations, along with the constants on the right side of the equations. Choice B correctly matches the coefficients and constants from the given system of equations, including the negative sign in front of the 12 in the first equation.

Question 3

Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { c c c c } 1 & 6 & 5 & - 1 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$ $\left[ \begin{array} { c c c c } 1 & 6 & \cdots & \cdots \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$

A)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

B)

\left[ \begin{array} { c c c c } 1 & 6 & - 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

C)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

D)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

E)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

Accepted Answer

&#8203; $$\left[ \begin{array} { c c c } &#10;2 & 3 & \frac { 4 } { 3 } \&#10;5 & - 4 & 7&#10;\end{array} \right]$$&#10;

Question 4

Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { c c c c } 1 & 6 & 5 & - 1 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$ $\left[ \begin{array} { c c c c } 1 & 6 & \cdots & \cdots \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$

A)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

B)

\left[ \begin{array} { c c c c } 1 & 6 & - 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

C)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

D)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

E)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

Accepted Answer

The answer of Fill in the blank(s)using elementary row operations...

Question 5

Select the system of linear equations represented by the following augmented matrix. $\left[\begin{array}{l}{\begin{array}{lllr}2 & 0 & 4 & \vdots-13\end{array}} \\\begin{array}{lllr}0 & 1&-2 & \vdots 6\end{array} \\\begin{array}{lllr}5 & 3 & 0 & \vdots 2\end{array} \\\end{array}\right]$

A)

\left\{ \begin{array} { r r } 2 x - 4 z = & 13 \\y - 2 z = & - 6 \\4 x + y = & 3\end{array} \right.

B)

\left\{\begin{aligned}2 x-4 z= & -13 \\y+2 z= & 6 \\4 x+y= & 3\end{aligned}\right.

C)

\left\{ \begin{array} { r r } x + y - 2 z = & - 13 \\x + y + 2 z = & 6 \\4 x + y + z = & 3\end{array} \right.

D)

\left\{ \begin{aligned}x - 2 z = & - 13 \\x - 2 z = & 6 \\4 x + y = & 3\end{aligned} \right.

E)

\left\{ \begin{array} { r r } 2 x + 4 z = & - 13 \\y - 2 z = & 6 \\5 x + 3 y = & 2\end{array} \right.

Accepted Answer

The augmented matrix directly translates to the system of equations in option D, with the first row representing $9x - 6y = 0$ and the second row representing $7x + 4y = -3$.

Question 6

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. ) $\left[\begin{array}{lll}1 & -4 & \vdots 6\\0 & 1 & \vdots -5\\\end{array} \right]$

A)

\left\{ \begin{aligned}x + 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,-5)

B)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,-5)

C)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,5)
D)

\left\{ \begin{aligned}x + 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-5,-14)
E)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-5,-14)

Accepted Answer

The augmented matrix corresponds to the system of equations $x - 4y = 6$ and $y = -5$. Substituting $y = -5$ into the first equation gives $x - 4(-5) = x + 20 = 6$, so $x = -14$. Therefore, the solution is $(-14, -5)$.

Question 7

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\- 5 & 4 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\11 & 0 & - 11\end{array} \right]$

A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.

Accepted Answer

The operation performed is adding 4 times the first row to the second row, which changes the second row to $11, 0, -11$.

Question 8

Select the augmented matrix for the system of linear equations.&#8203; $$\left\{ \begin{aligned}&#10;8 x - 4 y + z & = 14 \&#10;16 x - 9 z & = 12&#10;\end{aligned} \right.$$ &#8203;&#10;A)&#8203; $$\left[ \begin{array} { c c c c c } &#10;8 & - 4 & 1 & \vdots & 14 \&#10;16 & - 9 & 12 & \vdots & 0&#10;\end{array} \right]$$&#10;B)&#8203; $$\left[ \begin{array} { c c c c c } &#10;8 & - 4 & 1 & \vdots & 14 \&#10;16 & - 9 & 0 & \vdots & 12&#10;\end{array} \right]$$&#10;C)&#8203; $$\left[ \begin{array} { c c c c c } &#10;8 & 4 & 1 & \vdots & 14 \&#10;16 & 0 & - 9 & \vdots & 12&#10;\end{array} \right]$$&#10;D)&#8203; $$\left[ \begin{array} { c c c c c } &#10;8 & - 4 & 0 & \vdots & 14 \&#10;16 & 0 & 9 & \vdots & 12&#10;\end{array} \right]$$&#10;E)&#8203; $$\left[ \begin{array} { c c c  l } &#10;8 & - 4 & 1 & :14 \&#10;16 & 0 & - 9 & :12&#10;\end{array} \right]$$

Accepted Answer

The answer of Select the augmented matrix for the system...

Question 9

Select the system of linear equations represented by the following augmented matrix. $\left[\begin{array}{l}{\begin{array}{lllr}2 & 0 & 4 & \vdots-13\end{array}} \\\begin{array}{lllr}0 & 1&-2 & \vdots 6\end{array} \\\begin{array}{lllr}5 & 3 & 0 & \vdots 2\end{array} \\\end{array}\right]$

A)

\left\{ \begin{array} { r r } 2 x - 4 z = & 13 \\y - 2 z = & - 6 \\4 x + y = & 3\end{array} \right.

B)

\left\{\begin{aligned}2 x-4 z= & -13 \\y+2 z= & 6 \\4 x+y= & 3\end{aligned}\right.

C)

\left\{ \begin{array} { r r } x + y - 2 z = & - 13 \\x + y + 2 z = & 6 \\4 x + y + z = & 3\end{array} \right.

D)

\left\{ \begin{aligned}x - 2 z = & - 13 \\x - 2 z = & 6 \\4 x + y = & 3\end{aligned} \right.

E)

\left\{ \begin{array} { r r } 2 x + 4 z = & - 13 \\y - 2 z = & 6 \\5 x + 3 y = & 2\end{array} \right.

Accepted Answer

The augmented matrix directly translates to the system of equations in choice D, where the first row represents $x + 3y = 8$ and the second row represents $3x - 4y = 5$.

Question 10

Select the order for the following matrix.&#8203; $$\left[ \begin{array} { c c c c } &#10;- 3 & 5 & 10 & 0 \&#10;0 & 0 & 5 & 5 \&#10;4 & 4 & 8 & 5&#10;\end{array} \right]$$ &#8203;&#10;A)4 &#215; 3&#10;B)4 &#215; 2&#10;C)4 &#215; 4&#10;D)3 &#215; 3&#10;E)3 &#215; 4

Accepted Answer

The order of a matrix is given by the number of rows × the number of columns. This matrix has 3 rows and 4 columns, so its order is 3 × 4.

Question 11

Select the order for the following matrix.&#8203; $$\left[ \begin{array} { r r r } &#10;- 9 & 8 & 7 \&#10;0 & - 5 & 3&#10;\end{array} \right]$$ &#8203;&#10;A)2 &#215; 3&#10;B)3 &#215; 1&#10;C)3 &#215; 2&#10;D)3 &#215; 3&#10;E)2 &#215; 2

Accepted Answer

The answer of Select the order for the following matrix.&#8203;...

Question 12

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. ) $\left[\begin{array}{lll}1 & -4 & \vdots 6\\0 & 1 & \vdots -5\\\end{array} \right]$

A)

\left\{ \begin{aligned}x + 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,-5)

B)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,-5)

C)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-14,5)
D)

\left\{ \begin{aligned}x + 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-5,-14)
E)

\left\{ \begin{aligned}x - 4 y & = 6 \\y & = - 5\end{aligned} \right.

(-5,-14)

Accepted Answer

The answer of Find the system of linear equations represented...

Question 13

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\- 5 & 4 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\11 & 0 & - 11\end{array} \right]$

A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.

Accepted Answer

The answer of Identify the elementary row operation being performed...

Question 14

Determine whether the following matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. $\left[ \begin{array} { l l l l } 1 & 0 & 1 & 0 \\0 & 1 & 0 & 3 \\0 & 0 & 1 & 0\end{array} \right]$

A)Row-echelon form
B)Not in row-echelon form
C)Reduced row-echelon form

Accepted Answer

The answer of Determine whether the following matrix is in...

Question 15

Select the system of linear equations represented by the following augmented matrix. $\left[\begin{array}{l}{\begin{array}{lllr}2 & 0 & 4 & \vdots-13\end{array}} \\\begin{array}{lllr}0 & 1&-2 & \vdots 6\end{array} \\\begin{array}{lllr}5 & 3 & 0 & \vdots 2\end{array} \\\end{array}\right]$

A)

\left\{ \begin{array} { r r } 2 x - 4 z = & 13 \\y - 2 z = & - 6 \\4 x + y = & 3\end{array} \right.

B)

\left\{\begin{aligned}2 x-4 z= & -13 \\y+2 z= & 6 \\4 x+y= & 3\end{aligned}\right.

C)

\left\{ \begin{array} { r r } x + y - 2 z = & - 13 \\x + y + 2 z = & 6 \\4 x + y + z = & 3\end{array} \right.

D)

\left\{ \begin{aligned}x - 2 z = & - 13 \\x - 2 z = & 6 \\4 x + y = & 3\end{aligned} \right.

E)

\left\{ \begin{array} { r r } 2 x + 4 z = & - 13 \\y - 2 z = & 6 \\5 x + 3 y = & 2\end{array} \right.

Accepted Answer

The answer of Select the system of linear equations represented...

Question 16

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z and if applicable. ) $\left[\begin{array}{l}{\begin{array}{cccc}1 & -1 & 6 & \vdots8\end{array}} \\\begin{array}{llll}0 & 1 & -1 & \vdots6\end{array} \\\begin{array}{llll}0 & 0 & -1 & \vdots-6\end{array} \\\end{array}\right]$

A)

\left\{ \begin{aligned}x - y + 6 z & = 8 \\y + z & = 6 \\z & = - 6\end{aligned} \right.

(56,12,-6)
B)

\left\{ \begin{aligned}x - y + 6 z & = 8 \\y - z & = - 6 \\z & = 6\end{aligned} \right.

(44,0,-6)
C)

\left\{ \begin{array} { r } x - y + 6 z = 8 \\y + z = 6 \\z = 6\end{array} \right.

(-40,12,6)
D)

\left\{ \begin{aligned}x - y + 6 z & = 8 \\y - z & = 6 \\z & = - 6\end{aligned} \right.

(44,0,-6)
E)

\left\{ \begin{aligned}x - y + 6 z & = 8 \\y + z & = - 6 \\z & = 6\end{aligned} \right.

(-40,12,6)

Accepted Answer

The answer of Find the system of linear equations represented...

Question 17

Select the augmented matrix for the system of linear equations.&#8203; $$\left\{ \begin{aligned}&#10;6 x - 5 y & = - 7 \&#10;- x + 5 y & = 15&#10;\end{aligned} \right.$$ &#8203;&#10;A)&#8203; $$\left[ \begin{array} { c c : c } &#10;5 & - 6 & - 7 \&#10;5 & - 1 & 15&#10;\end{array} \right]$$&#10;B) $\left[\begin{array}{cc:c}&#10;6 & 5 & -7 \&#10;-1 & 5 & 15&#10;\end{array}\right]$&#10;C) $\left[\begin{array}{cc:c}&#10;6 & 5 & 7 \&#10;1 & 5 & 15&#10;\end{array}\right]$&#10;D) $\left[\begin{array}{cccc}&#10;6 & -5 & \vdots & -7 \&#10;-1 & 5 & \vdots & 15&#10;\end{array}\right]$&#10;E) $\left[\begin{array}{cc:c}&#10;5 & 6 & 7 \&#10;5 & -1 & 15&#10;\end{array}\right]$

Accepted Answer

The answer of Select the augmented matrix for the system...

Question 18

Perform the sequence of row operations on the following matrix. Add -3 times R₁ to R₂. $$\left[ \begin{array} { c c c } 1 & 3 & 4 \ 3 & - 1 & - 5 \ 4 & 1 & - 1 \end{array} \right]$$ A) $$\left[ \begin{array} { c c c } 1 & 3 & 4 \ 0 & 4 & - 17 \ 4 & 1 & - 1 \end{array} \right]$$ B) $$\left[ \begin{array} { c c c } 1 & 3 & 4 \ 0 & - 10 & - 17 \ 4 & 1 & - 1 \end{array} \right]$$ C) $$\left[ \begin{array} { c c c } 1 & 3 & 4 \ 0 & - 10 & 3 \ 4 & 1 & - 1 \end{array} \right]$$ D) $$\left[ \begin{array} { c c c } - 1 & 3 & 4 \ 0 & - 10 & - 17 \ 4 & - 1 & - 1 \end{array} \right]$$ E) $$\left[ \begin{array} { c c c } 1 & 3 & 4 \ 0 & 1 & - 17 \ 4 & 1 & - 1 \end{array} \right]$$

Accepted Answer

The answer of Perform the sequence of row operations on...

Question 19

Perform the sequence of row operations on the following matrix. Add R₃to R₄. $$\left[ \begin{array} { c c } 7 & 1 \ 0 & 2 \ - 3 & 4 \ 4 & 1 \end{array} \right]$$ A) $$\left[ \begin{array} { l l } 7 & 1 \ 0 & 2 \ 7 & 5 \ 4 & 1 \end{array} \right]$$ B) $$\left[ \begin{array} { c c } 7 & 1 \ 0 & 2 \ - 3 & 4 \ 11 & 7 \end{array} \right]$$ C) $$\left[ \begin{array} { l l } 7 & 1 \ 0 & 2 \ 1 & 5 \ 4 & 1 \end{array} \right]$$ D) $$\left[ \begin{array} { c c } 7 & 1 \ 0 & 2 \ - 3 & 4 \ 7 & 11 \end{array} \right]$$ E) $$\left[ \begin{array} { c c } 7 & 1 \ 0 & 2 \ - 3 & 4 \ 1 & 5 \end{array} \right]$$

Accepted Answer

The answer of Perform the sequence of row operations on...

Question 20

Fill in the blank(s)using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { c c c c } 1 & 6 & 5 & - 1 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$ $\left[ \begin{array} { c c c c } 1 & 6 & \cdots & \cdots \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$

A)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

B)

\left[ \begin{array} { c c c c } 1 & 6 & - 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

C)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

D)

\left[ \begin{array} { c c c c } 1 & 6 & 17 & - 13 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

E)

\left[ \begin{array} { c c c c } 1 & 0 & - 1 & - 7 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]

Accepted Answer

The answer of Fill in the blank(s)using elementary row operations...

Question 21

An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. $\left[\begin{array}{lll}1 & 0 & \vdots 5\\0 & 1 & \vdots -6\\\end{array} \right]$

A)(-6,7)
B)(-6,5)
C)(-5,6)
D)(5,-6)
E)(6,5)

Accepted Answer

The answer of An augmented matrix that represents a system...

Question 22

Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. $\left[ \begin{array} { r r r r } 1 & 9 & - 9 & - 6 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & 1\end{array} \right]$

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither

Accepted Answer

The answer of Determine whether the matrix is in row-echelon...

Question 23

Determine the order of the matrix.&#8203; $$\left[ \begin{array} { l l l } &#10;4 & 3 & - 8&#10;\end{array} \right]$$ &#8203;&#10;A)1 &#215; 1&#10;B)3&#10;C)3 &#215; 3&#10;D)3 &#215; 1&#10;E)1 &#215; 3

Accepted Answer

The answer of Determine the order of the matrix.&#8203; \[\left[...

Question 24

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

Accepted Answer

The answer of Use matrices to solve the system of...

Question 25

Write the augmented matrix for the system of linear equations. $$\left\{ \begin{aligned}&#10;x - 3 y - 2 z & = - 2 \&#10;4 y + 4 z & = 4 \&#10;x + 4 z & = - 2&#10;\end{aligned} \right.$$&#10;A) $$\left[ \begin{array} { c c c c c } &#10;1 & - 3 & - 2 & \vdots & - 2 \&#10;0 & 4 & 4 & \vdots & 4 \&#10;1 & 4 & 0 & \vdots & - 2&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { c c c c c } &#10;1 & - 3 & - 2 & \vdots & - 2 \&#10;4 & 44 & 0 & \vdots & 4 \&#10;1 & 4 & 0 & \vdots & - 2&#10;\end{array} \right]$$&#10;C) $$\left[ \begin{array} { c c c c c } &#10;1 & - 3 & - 2 & \vdots & - 2 \&#10;1 & 4 & 4 & \vdots & 4 \&#10;1 & 1 & 4 & \vdots & - 2&#10;\end{array} \right]$$&#10;D) $$\left[ \begin{array} { c c c c c } &#10;1 & - 3 & - 2 & \vdots & - 2 \&#10;& 4 & 4 & \vdots & 4 \&#10;1 & & 4 & \vdots & - 2&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { c c c c c } &#10;1 & - 3 & - 2 & \vdots & - 2 \&#10;0 & 4 & 4 & \vdots & 4 \&#10;1 & 0 & 4 & \vdots & - 2&#10;\end{array} \right]$$ &#8203;

Accepted Answer

The answer of Write the augmented matrix for the system...

Question 26

The currents in an electrical network are given by the solution of the system $\left\{ \begin{aligned}I _ { 1 } - I _ { 2 } + I _ { 3 } & = 5 \\3 I _ { 1 } + 4 I _ { 2 } & = 19 \\I _ { 2 } + 3 I _ { 3 } & = 28\end{aligned} \right.$ where I₁,I₂ and I₃ are measured in amperes.Solve the system of equations using matrices.

A)I₁ = 5,I₂ = 4,I₃ = 8
B)I₁ = 4,I₂ = 4,I₃ = 8
C)I₁ = 3,I₂ = 4,I₃ = 8
D)I₁ = 2,I₂ = 4,I₃ = 8
E)I₁ = 1,I₂ = 4,I₃ = 8

Accepted Answer

The answer of The currents in an electrical network are...

Question 27

An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. $\left[\begin{array}{l}{\begin{array}{cccc}1 & 0 & 0 & \vdots-3\end{array}} \\\begin{array}{llll}0 & 1 & 0 & \vdots-9\end{array} \\\begin{array}{llll}0 & 0 & 1 & \vdots3\end{array} \\\end{array}\right]$

A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)

Accepted Answer

The answer of An augmented matrix that represents a system...

Question 28

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

Accepted Answer

The answer of Use matrices to solve the system of...

Question 29

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r r } &#10;5 & - 7 & - 3 & 6 \&#10;- 6 & - 6 & 2 & - 44 \&#10;2 & - 4 & - 2 & - 4&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 6 \&#10;0 & 1 & 0 & 3 \&#10;0 & 0 & 1 & 5&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 1 \&#10;0 & 1 & 0 & 1 \&#10;0 & 0 & 1 & 1&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 7 \&#10;0 & 1 & 0 & 2 \&#10;0 & 0 & 1 & 5&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 0 \&#10;0 & 1 & 0 & 0 \&#10;0 & 0 & 1 & 0&#10;\end{array} \right]$$&#10;E) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 7 \&#10;0 & 1 & 0 & 5 \&#10;0 & 0 & 1 & 2&#10;\end{array} \right]$$ &#8203;

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Question 30

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { r l r } 3 x + 2 y - z + w & = 0 \\x - y + 4 z - w & = 28 \\- 2 x + y + 2 z - w & = 3 \\x + y + z + w & = 8\end{array} \right.$

A)(-3,-2,6,1)
B)(-3,2,-6,-1)
C)(3,-2,6,1)
D)(3,-2,6,-1)
E)(3,-2,-6,1)

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Question 31

Fill in the blank using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { r r r } 2 & 1 & - 2 \\- 10 & - 1 & 9\end{array} \right]$ $\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & \square & - 1\end{array} \right]$

A)

\left[ \begin{array} { c c c } 2 & 1 & - 2 \\0 & - 6 & - 1\end{array} \right]

B)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 4 & - 1\end{array} \right]

C)

\left[ \begin{array} { r r r } 2 & 1 & - 2 \\0 & - 4 & - 1\end{array} \right]

D)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 1 & - 1\end{array} \right]

E)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 0 & - 1\end{array} \right]

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Question 32

An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. $\left[\begin{array}{l}{\begin{array}{cccc}1 & 0 & 0 & \vdots-3\end{array}} \\\begin{array}{llll}0 & 1 & 0 & \vdots-9\end{array} \\\begin{array}{llll}0 & 0 & 1 & \vdots3\end{array} \\\end{array}\right]$

A)(-3,9,3)
B)(3,-9,3)
C)(-3,-9,3)
D)(-3,-9,-3)
E)(-3,3,-9)

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Question 33

Use matrices to find the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}5 x - 5 y & = 5 \\- 2 x - 3 y & = 18\end{aligned} \right.$

A)(3,4)
B)(-3,4)
C)(5,18)
D)(-3,-4)
E)(3,-4)

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Question 34

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

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Question 35

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

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Question 36

Determine the order of the matrix.&#8203; $$\left[ \begin{array} { l l l } &#10;8 & 5 & 4 \&#10;7 & 8 & 1&#10;\end{array} \right]$$ &#8203;&#10;A)3 &#215; 3&#10;B)2 &#215; 2&#10;C)3 &#215; 1&#10;D)2 &#215; 3&#10;E)3 &#215; 2

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Question 37

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\- 5 & 4 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\11 & 0 & - 11\end{array} \right]$

A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.

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Question 38

Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system. $\left\{ \begin{aligned}x + 2 y + 2 z + 4 w & = 20 \\3 x + 6 y + 5 z + 12 w & = 53 \\x + 3 y - 3 z + 2 w & = - 18 \\6 x - y - z + w & = - 30\end{aligned} \right.$

A)(-4,1,7,-2)
B)(-4,-1,7,2)
C)(-4,1,-7,2)
D)(-4,-1,-7,-2)
E)(-4,1,7,2)

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Question 39

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { r l c } - x + y - z & = - 20 \\2 x - y + z & = 29 \\3 x + 2 y + z & = 29\end{array} \right.$

A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)

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Question 40

Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. ) $\left[\begin{array}{l}{\begin{array}{lllll}-1 & 0 & 0 &3&\vdots2\end{array}} \\\begin{array}{lllll}-7 & 4 & 0 &0& \vdots8\end{array} \\\begin{array}{lllll}0 & 5 & 3 &-5& \vdots-8\end{array} \\\begin{array}{lllll}0 & 0 & -1 &-9& \vdots9\end{array} \\\end{array}\right]$

A)

\left\{ \begin{array} { r l r } - x + 3 w & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- y - 9 z & = 9\end{array} \right.

B)

\left\{ \begin{array} { r l r } - x + 3 z & = 2 \\- 7 x + 4 z & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{array} \right.

C)

\left\{ \begin{array} { r l r } - x + 3 y & = & 2 \\- 7 x + 4 y & = & 8 \\5 x + 3 y - 5 z & = - 8 \\- x - 9 y & = 9\end{array} \right.

D)

\left\{ \begin{aligned}- x + 3 w & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{aligned} \right.

E)

\left\{ \begin{array} { r l r } - x + 3 z & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{array} \right.

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Question 41

Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. $\left[ \begin{array} { r r r r } 1 & 9 & - 9 & - 6 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & 1\end{array} \right]$

A)row-echelon form
B)row-echelon form and reduced row-echelon form
C)neither

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Question 42

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

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Question 43

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}x - 4 y + 3 z - 2 w & = 10 \\3 x - 2 y + z - 4 w & = - 22 \\- 4 x + 3 y - 2 z + w & = - 2 \\- 2 x + y - 4 z + 3 w & = - 10\end{aligned} \right.$

A)(-2,-1,8,6)
B)(-2,0,8,6)
C)(-2,0,8,-6)
D)(-2,-1,-8,-6)
E)(-2,0,-8,6)

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Question 44

Use a system of equations to find the specified equation that passes through the points.Solve the system using matrices. Parabola: y = ax² + bx + c A) $y = 2 x ^ { 2 } - x + 6$ B) $y = - x ^ { 2 } + 6$ C) $y = - x ^ { 2 } + x + 6$ D) $y = + x ^ { 2 } + 6$ E) $y = - x ^ { 2 } - x + 6$

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Question 45

Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. ) $\left[\begin{array}{l}{\begin{array}{lllll}-1 & 0 & 0 &3&\vdots2\end{array}} \\\begin{array}{lllll}-7 & 4 & 0 &0& \vdots8\end{array} \\\begin{array}{lllll}0 & 5 & 3 &-5& \vdots-8\end{array} \\\begin{array}{lllll}0 & 0 & -1 &-9& \vdots9\end{array} \\\end{array}\right]$

A)

\left\{ \begin{array} { r l r } - x + 3 w & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- y - 9 z & = 9\end{array} \right.

B)

\left\{ \begin{array} { r l r } - x + 3 z & = 2 \\- 7 x + 4 z & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{array} \right.

C)

\left\{ \begin{array} { r l r } - x + 3 y & = & 2 \\- 7 x + 4 y & = & 8 \\5 x + 3 y - 5 z & = - 8 \\- x - 9 y & = 9\end{array} \right.

D)

\left\{ \begin{aligned}- x + 3 w & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{aligned} \right.

E)

\left\{ \begin{array} { r l r } - x + 3 z & = 2 \\- 7 x + 4 y & = 8 \\5 y + 3 z - 5 w & = - 8 \\- z - 9 w & = 9\end{array} \right.

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Question 46

Perform the sequence of row operations on the matrix.What did the operations accomplish? $\left[ \begin{array} { c c c } 1 & 1 & - 7 \\4 & 5 & - 7 \\1 & 3 & 35\end{array} \right]$ Add -4 times R₁ to R₂,
Add -1 times R₁ to R₃,
Add -2 times R₂ to R₃,
Add -1 times R₂ to R₁.

A)

\left[ \begin{array} { l l l } 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array} \right]

The operations produce a row-equivalent matrix in reduced row-echelon form.
B)

\left[ \begin{array} { r r r } 1 & 0 & - 28 \\0 & 1 & 21 \\0 & 0 & 0\end{array} \right]

The operations produce a row-equivalent matrix in reduced row-echelon form.
C)

\left[ \begin{array} { r r r } 1 & 1 & - 28 \\0 & 1 & 21 \\0 & 0 & 0\end{array} \right]

The operations produce a row-equivalent matrix in reduced row-echelon form.
D)

\left[ \begin{array} { c c c } 1 & 1 & - 7 \\0 & 1 & 21 \\0 & 2 & 42\end{array} \right]

The operations produce a row-equivalent matrix in reduced row-echelon form.
E)

\left[ \begin{array} { r r r } 1 & 0 & - 28 \\0 & 0 & 21 \\0 & 0 & 0\end{array} \right]

The operations produce a row-equivalent matrix in reduced row-echelon form.

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Question 47

Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. $\left\{ \begin{aligned}x - y - 6 z & = - 33 \\y + 3 z & = 18 \\z & = 4\end{aligned} \right.$ $\left\{ \begin{array} { r l r } x - 7 y - 3 z & = - 57 \\y - 9 z & = - 30 \\z & = 4\end{array} \right.$

A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3

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Question 48

Write the augmented matrix for the system of linear equations. $$\left\{ \begin{aligned}&#10;x + 7 y + 7 z & = - 6 \&#10;3 y + 3 z & = 6 \&#10;x + 7 z & = - 7&#10;\end{aligned} \right.$$&#10;A) $$\left[ \begin{array} { r r r r r } &#10;1 & 7 & 7 & \vdots & - 6 \&#10;1 & 3 & 3 & \vdots & 6 \&#10;1 & 1 & 7 & \vdots & - 7&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { r r r r r } &#10;1 & 7 & 7 & \vdots & - 6 \&#10;1 & 3 & 3 & \vdots & 6 \&#10;1 & 0 & 7 & \vdots & - 7&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { r r r r r } &#10;1 & 7 & 7 & \vdots & - 6 \&#10;& 3 & 3 & \vdots & 6 \&#10;1 & & 7 & \vdots & - 7&#10;\end{array} \right]$$ &#8203;&#10;D) $\left[\begin{array}{rrrrr}&#10;1 & 7 & 7 & \vdots & -6 \&#10;3 & 33 & 0 & \vdots & 6 \&#10;1 & 7 & 0 & \vdots & -7&#10;\end{array}\right]$ &#8203;&#10;E) $$\left[ \begin{array} { r r r r r } &#10;1 & 7 & 7 & \vdots & - 6 \&#10;0 & 3 & 3 & \vdots & 6 \&#10;1 & 7 & 0 & \vdots & - 7&#10;\end{array} \right]$$

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Question 49

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r } &#10;4 & 5 & 11 \&#10;3 & 1 & - 11 \&#10;3 & 5 & 17&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { r r r } &#10;1 & 0 & - 6 \&#10;0 & 0 & 0 \&#10;0 & 0 & 0&#10;\end{array} \right]$$&#10;B) $$\left[ \begin{array} { l l l } &#10;1 & 0 & 0 \&#10;0 & 1 & 0 \&#10;0 & 0 & 0&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 4 \&#10;0 & 1 & 5 \&#10;0 & 0 & 1&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { c c c } &#10;1 & 0 & - 7 \&#10;0 & 1 & - 6 \&#10;0 & 0 & 0&#10;\end{array} \right]$$ &#8203;&#10;E) $$\left[ \begin{array} { r r r } &#10;1 & 0 & - 6 \&#10;0 & 1 & 7 \&#10;0 & 0 & 0&#10;\end{array} \right]$$ &#8203;

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Question 50

Determine the order of the matrix. $$\left[ \begin{array} { r r r } &#10;6 & - 7 & 7 \&#10;9 & 6 & 7&#10;\end{array} \right]$$&#10;A)2 &#215; 3&#10;B)3 &#215; 3&#10;C)3 &#215; 1&#10;D)3 &#215; 2&#10;E)2 &#215; 2

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Question 51

An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. $\left[\begin{array}{l}{\begin{array}{cccc}1 & 0 & 0 & \vdots8\end{array}} \\\begin{array}{llll}0 & 1 & 0 & \vdots-6\end{array} \\\begin{array}{llll}0 & 0 & 1 & \vdots0\end{array} \\\end{array}\right]$

A)(0,8,-6)
B)(8,0,-6)
C)(8,-6,0)
D)(-8,-6,0)
E)(8,6,0)

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Question 52

Identify the elementary row operation being performed to obtain the new row-equivalent matrix.
Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\- 5 & 4 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\11 & 0 & - 11\end{array} \right]$

A)Add 4 times Row 2 to Row 1.
B)Add 5 times Row 2 to Row 1.
C)Add 9 times Row 1 to Row 2.
D)Add 4 times Row 1 to Row 2.
E)Add 5 times Row 1 to Row 2.

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Question 53

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) $\left[\begin{array}{rrrrrr}&#10;1 & 2 & 5 & \vdots & 34 \&#10;0 & 1 & 2 & \vdots & 14 \&#10;0 & 0 & 1 & \vdots & 5&#10;\end{array}\right]$&#10;A)x = 35,y = -3,z = 1&#10;B)x = 4,y = 1,z = 5&#10;C)x = 1,y = -4,z = -5&#10;D)x = 1,y = 4,z = 5&#10;E)x = -4,y = 5,z = -1

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Question 54

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { r l c } - x + y - z & = - 20 \\2 x - y + z & = 29 \\3 x + 2 y + z & = 29\end{array} \right.$

A)(-9,-3,8)
B)(-9,-3,-8)
C)(9,-3,8)
D)(9,-3,-8)
E)(9,3,8)

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Question 55

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) $$\left[ \begin{array} { r r r r r } &#10;1 & 9 & - 3 &\vdots& - 39 \&#10;0 & 1 & 2 & \vdots & 0 \&#10;0 & 0 & 1 & \vdots & 2&#10;\end{array} \right]$$&#10;A)x = 4,y = 2,z = -3&#10;B)x = 3,y = -4,z = 2&#10;C)x = 3,y = 4,z = -2&#10;D)x = -18,y = -1,z = 4&#10;E)x = -4,y = 3,z = 2

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Question 56

Fill in the blank using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { r r r } 2 & 1 & - 2 \\- 10 & - 1 & 9\end{array} \right]$ $\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & \square & - 1\end{array} \right]$

A)

\left[ \begin{array} { c c c } 2 & 1 & - 2 \\0 & - 6 & - 1\end{array} \right]

B)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 4 & - 1\end{array} \right]

C)

\left[ \begin{array} { r r r } 2 & 1 & - 2 \\0 & - 4 & - 1\end{array} \right]

D)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 1 & - 1\end{array} \right]

E)

\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & 0 & - 1\end{array} \right]

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Question 57

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { c } 4 x + 9 y + z = - 17 \\6 x - 6 y - 8 z = 12 \\9 x + 8 y + z = - 43\end{array} \right.$

A)x = 5,y = -1,z = -6
B)x = -5,y = -1,z = -6
C)x = -5,y = 1,z = -6
D)x = 1,y = 5,z = 6
E)no solution

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Question 58

Write the matrix in reduced row-echelon form. $$\left[ \begin{array} { r r r r } &#10;9 & - 6 & - 3 & - 33 \&#10;8 & - 1 & 1 & - 47 \&#10;- 7 & - 7 & 6 & - 8&#10;\end{array} \right]$$&#10;A) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 0 \&#10;0 & 1 & 0 & 0 \&#10;0 & 0 & 1 & 0&#10;\end{array} \right]$$ &#8203;&#10;B) $$\left[ \begin{array} { l l l r } &#10;1 & 0 & 0 & - 5 \&#10;0 & 1 & 0 & - 6 \&#10;0 & 0 & 1 & 1&#10;\end{array} \right]$$ &#8203;&#10;C) $$\left[ \begin{array} { r r r r } &#10;1 & 0 & 0 & - 6 \&#10;0 & 1 & 0 & 2 \&#10;0 & 0 & 1 & - 6&#10;\end{array} \right]$$ &#8203;&#10;D) $$\left[ \begin{array} { r r r r } &#10;1 & 0 & 0 & - 5 \&#10;0 & 1 & 0 & 1 \&#10;0 & 0 & 1 & - 6&#10;\end{array} \right]$$ &#8203;&#10;E) $$\left[ \begin{array} { l l l l } &#10;1 & 0 & 0 & 1 \&#10;0 & 1 & 0 & 1 \&#10;0 & 0 & 1 & 1&#10;\end{array} \right]$$

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Question 59

Determine whether the two systems of linear equations yield the same solutions.If so,find the solutions using matrices. $\left\{ \begin{aligned}x - y - 6 z & = - 33 \\y + 3 z & = 18 \\z & = 4\end{aligned} \right.$ $\left\{ \begin{array} { r l r } x - 7 y - 3 z & = - 57 \\y - 9 z & = - 30 \\z & = 4\end{array} \right.$

A)x = -3,y = 6,z = 4
B)The systems yield different solutions.
C)x = 3,y = 4,z = -3
D)x = 3,y = -6,z = 4
E)x = 6,y = 4,z = -3

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Question 60

The currents in an electrical network are given by the solution of the system $\left\{ \begin{aligned}I _ { 1 } - I _ { 2 } + I _ { 3 } & = 5 \\3 I _ { 1 } + 4 I _ { 2 } & = 19 \\I _ { 2 } + 3 I _ { 3 } & = 28\end{aligned} \right.$ where I₁,I₂ and I₃ are measured in amperes.Solve the system of equations using matrices.

A)I₁ = 5,I₂ = 4,I₃ = 8
B)I₁ = 4,I₂ = 4,I₃ = 8
C)I₁ = 3,I₂ = 4,I₃ = 8
D)I₁ = 2,I₂ = 4,I₃ = 8
E)I₁ = 1,I₂ = 4,I₃ = 8

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Question 61

The currents in an electrical network are given by the solution of the system $\left\{ \begin{aligned}I _ { 1 } - I _ { 2 } + I _ { 3 } & = 5 \\3 I _ { 1 } + 4 I _ { 2 } & = 19 \\I _ { 2 } + 3 I _ { 3 } & = 28\end{aligned} \right.$ where I₁,I₂ and I₃ are measured in amperes.Solve the system of equations using matrices.

A)I₁ = 5,I₂ = 4,I₃ = 8
B)I₁ = 4,I₂ = 4,I₃ = 8
C)I₁ = 3,I₂ = 4,I₃ = 8
D)I₁ = 2,I₂ = 4,I₃ = 8
E)I₁ = 1,I₂ = 4,I₃ = 8

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Question 62

Solve the system using Gauss-Jordan elimination.&#8203; $$\left\{ \begin{aligned}&#10;x + y + 2 z + t & = 62 \&#10;x + 2 y + z + t & = 62 \&#10;2 x + y + z + t & = 49 \&#10;x + y + z + 2 t & = 62&#10;\end{aligned} \right.$$ &#8203;&#10;A) $( 2 , - 15,15 , - 15 )$ &#8203;&#10;B) $( - 2,15,15,15 )$ &#8203;&#10;C) $( 2 , - 15,15,15 )$ &#8203;&#10;D) $( 2,15,15,15 )$ &#8203;&#10;E) $( 2,15 , - 15,15 )$ &#8203;

Accepted Answer

The answer of Solve the system using Gauss-Jordan elimination.&#8203; \[\left\{...

Question 63

Solve the system by Gauss - Jordan elimination.&#8203; $$\left\{ \begin{aligned}&#10;\frac { 1 } { 3 } x + \frac { 3 } { 4 } y - \frac { 2 } { 3 } z & = - 4 \&#10;x + \frac { 1 } { 2 } y + \frac { 1 } { 3 } z & = 30 \&#10;\frac { 1 } { 6 } x - \frac { 1 } { 8 } y - z & = - 30&#10;\end{aligned} \right.$$ &#8203;&#10;A) $( - 12 , - 16 , - 30 )$ &#8203;&#10;B) $( - 12,16 , - 30 )$ &#8203;&#10;C) $( 12,16,30 )$ &#8203;&#10;D) $( 0,16 , - 30 )$ &#8203;&#10;E) $( 12 , - 16,30 )$ &#8203;

Accepted Answer

The answer of Solve the system by Gauss - Jordan...

Question 64

Solve the system using Gauss-Jordan elimination.&#8203; $$\left\{ \begin{array} { l } &#10;w + x = 9 \&#10;w + y = 0 \&#10;x + z = 0&#10;\end{array} \right.$$&#10;A) $$w = - 9 + z , x = - z , y = - 9 - z , z$$&#10;B) $w = 9 + z , x = - z , y = - 9 - z , z$&#10;C) $$w = 9 + z , x = - z , y = 9 - z , z$$ &#8203;&#10;D) $w = 9 + z , x = - z , y = 9 + z , z$ &#8203;&#10;E) $w = 9 - z , x = - z , y = - 9 - z , z$ &#8203;

Accepted Answer

The answer of Solve the system using Gauss-Jordan elimination.&#8203; \[\left\{...

Deck 47: Matrices and Systems of Equations