Question 1

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place.
-$ 2.6 x-0.7 y+5.3 z-3.4 w=12.9 $
$ 6.5 \mathrm{y} \quad+0.7 \mathrm{w}=-1.8 $
$ 4.0 z-2.2 w=1.5 $
$ 4.9 x+0.6 w=3.2 $
A) $ (2.2,1.1,7.2,12.4) $
B) $ (-2.2,1.1,-6.4,23.3) $
C) $ (2.2,1.1,-6.4,-12.4) $
D) $ (2.2,-1.1,-6.4,7.6) $

Accepted Answer

The solution to the system of equations, when solved using a graphing calculator, is $ (2.2,1.1,-6.4,-12.4) $.

Question 2

Use the Gauss-Jordan method to solve the system of equations.
-$
5 x-3 y=6
$
$ 25 x-15 y=9 $
A) $ (6,9) $
B) $ \left(\frac{6}{5}+\frac{3}{5} y, y\right) $
C) $ (5,5) $
D) No solution

Accepted Answer

The second equation is a multiple of the first (multiplied by 5), which means the two equations are actually the same line. Therefore, there are infinitely many solutions, but in the context of the given options, it means there is no single solution to be selected from the choices provided.

Question 3

Find the ratios of products A, B, and C using a closed model.
-
A) 13: 25: 100
B) $ 33: 67: 63 $
C) 1: $ 149: 100 $
D) 1: 25: 25

Accepted Answer

The answer of Find the ratios of products A, B,...

Question 4

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist.
-$$
\begin{array}{l}
3 x+y=15 \
2 x+4 y=0
\end{array}
$$
A) $ (-3,-6) $
B) $ (6,-3) $
C) $ (-3,6) $
D) No inverse, no solution for system

Accepted Answer

The system of equations can be solved using the inverse of the coefficient matrix. The coefficient matrix is $\begin{pmatrix} 3 & 1 \ 2 & 4 \end{pmatrix}$, and its inverse exists. By calculating the inverse and applying it to the constants (15, 0), we find the solution $ (6, -3) $.

Question 5

Find the production matrix for the input-output and demand matrices using the open model.
-$$
A=\left[\begin{array}{ll}
0.2 & 0.1 \
0.5 & 0.4
\end{array}\right], D=\left[\begin{array}{l}
3 \
6
\end{array}\right]
$$
A) $ \left[\begin{array}{r}5.13 \ 14.65\end{array}\right] $
B) $ \left[\begin{array}{r}5.58 \ 14.65\end{array}\right] $
C) $ \left[\begin{array}{l}5.55 \ 7.88\end{array}\right] $
D) $ \left[\begin{array}{r}6.98 \ 18.31\end{array}\right] $

Accepted Answer

The production matrix $ X $ is found using the formula $ X = (I - A)^{-1}D $. First, calculate $ I - A $, then find its inverse, and multiply by $ D $. The correct result is $ \left[\begin{array}{r}5.58 \ 14.65\end{array}\right] $.

Question 6

Solve the problem.
-A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers J and K. What is The cost of 100 batches of each candy using ingredients from supplier K?

A) $ \$ 12.000 $
B) $ \$ 15.200 $
C) $ \$ 6000 $
D) $ \$ 9400 $

Accepted Answer

The answer of Solve the problem.
-A company makes three chocolate...

Question 7

Solve the problem.
-Suppose the following matrix represents the input-output matrix, T, of a simplified economy.  Find the amount of each commodity that should be produced.
A)3360 units of manufacturing, 2796 units of agriculture, and 3012 units of transportation.
B)2976 units of manufacturing, 3386.4 units of agriculture, and 2791.2 units of transportation.
C)3012 units of manufacturing, 3360 units of agriculture, and 2791.2 units of transportation.
D)3012 units of manufacturing, 2796 units of agriculture, and 2976 units of transportation.

Accepted Answer

The answer of Solve the problem.
-Suppose the following matrix represents...

Question 8

-

Accepted Answer

The answer of 
-...

Question 9

Solve the system of equations by using the inverse of the coefficient matrix.
-$$
\begin{array}{l}
x-y+z=-7 \
x+y+z=1 \
x+y-z=-1
\end{array}
$$
A) $ (-4,1,4) $
B) $ (1,-4,4) $
C) $ (-4,4,1) $
D) No inverse, no solution for system

Accepted Answer

The answer of Solve the system of equations by using...

Question 10

Find the ratios of products A, B, and C using a closed model.
-
A) $ 4: 8: 3 $
B) $ 3: 2: 3 $
C) $ 8: 16: 3 $
D) $ 3: 3: 2 $

Accepted Answer

The answer of Find the ratios of products A, B,...

Question 11

- AB is a 2 × 2 matrix.

Accepted Answer

The answer of 
- AB is a 2 × 2...

Question 12

Use a graphing calculator to find the matrix product and/or sum.
-Find $ \mathrm{AB} $.
$$
A=\left[\begin{array}{rrrr}
18 & 14 & 18 & 18 \
30 & 5 & 7 & 2 \
11 & 3 & 2 & 1 \
5 & 32 & 5 & 7
\end{array}\right] B=\left[\begin{array}{rrr}
18 & 5 & 3 \
18 & 8 & 12 \
7 & 4 & 2 \
21 & 15 & 13
\end{array}\right]
$$
A)  $ \left[\begin{array}{rrrr}468 & 364 & 468 & 468 \ 1140 & 190 & 266 & 76 \ 143 & 39 & 26 & 13 \ 245 & 1568 & 245 & 343\end{array}\right] $
B) $ \left[\begin{array}{rrr}1224 & 340 & 134 \ 792 & 352 & 528 \ 119 & 68 & 34 \ 1029 & 735 & 637\end{array}\right] $
C) $ \left[\begin{array}{rrr}1080 & 544 & 492 \ 721 & 248 & 190 \ 287 & 102 & 86 \ 848 & 406 & 500\end{array}\right] $
D) Does not exist

Accepted Answer

The matrix product $ \mathrm{AB} $ is calculated by multiplying matrix $ A $ (4x4) with matrix $ B $ (4x3), resulting in a 4x3 matrix. The correct product is option C.

Question 13

Use the Gauss-Jordan method to solve the system of equations.
-$
\begin{array}{l}
x-y+z=4 \
x+y+z=-2 \
x+y-z=-12
\end{array}
$
A) $ (-4,5,-3) $
B) $ (-4,-3,5) $
C) $ (5,-4,-3) $
D) No solution

Accepted Answer

The answer of Use the Gauss-Jordan method to solve the...

Question 14

For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers.
-$$
\begin{array}{r}
x+3 y+4 z=80 \
4 y+5 z=40
\end{array}
$$
A) 2
B) 4
C) 3
D) 5

Accepted Answer

The system of equations can be solved using the method of substitution or elimination. Since the equations are already in echelon form, we can start by solving the second equation for $y$ in terms of $z$, and then substitute that expression into the first equation to solve for $x$ in terms of $z$. The number of nonnegative integer solutions depends on the values of $z$ that make $x$ and $y$ nonnegative integers. By systematically trying values of $z$ that satisfy the second equation with nonnegative integers for $y$ and then checking if those lead to nonnegative integer values for $x$, we find there are 3 such solutions.

Question 15

Find the inverse, if it exists, for the matrix.
-
A)$ \left[\begin{array}{l}-\frac{2}{5} \frac{3}{5} \ -\frac{1}{2} \frac{1}{2}\end{array}\right] $
B)$ \left[\begin{array}{cc}\frac{3}{5} & \frac{1}{2} \ -\frac{2}{5} & -\frac{1}{2}\end{array}\right] $
C)$ \left[\begin{array}{l}-\frac{1}{2} \frac{1}{2} \ -\frac{2}{5} \frac{3}{5}\end{array}\right] $
D)$ \left[\begin{array}{rr}-\frac{1}{2} & -\frac{1}{2} \ \frac{2}{5} & \frac{3}{5}\end{array}\right] $
00

Accepted Answer

The answer of Find the inverse, if it exists, for...

Question 16

Find the ratios of products A, B, and C using a closed model.
-
A) $ 6: 3: 3 $
B) $ 1: 3: 3 $
C) $ 2: 3: 3 $
D) $ 3: 2: 3 $

Accepted Answer

The answer of Find the ratios of products A, B,...

Question 17

Solve the system of equations by using the inverse of the coefficient matrix.
-$$
\begin{array}{l}
9 x-2 y+5 z=78 \
2 x+3 y-9 z=-50 \
3 x-8 y+6 z=49
\end{array}
$$
A) $ (6,-1,7) $
B) $ (1,7,1) $
C) $ (5,-1,-7) $
D) $ (5,1,7) $

Accepted Answer

The answer of Solve the system of equations by using...

Question 18

Provide an appropriate response.
-True or False?

Accepted Answer

The answer of Provide an appropriate response.
-True or False? ...

Question 19

Use the indicated row operation to change the matrix.
-Replace $ R_{2} $ by $ R_{1}+R_{2} $.
$ \left[\begin{array}{rr|r}1 & 0 & 2 \ -1 & 1 & 3\end{array}\right] $
A) $ \left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 0 & 5\end{array}\right] $
B) $ \left[\begin{array}{rr|r}1 & 0 & 2 \ -1 & 1 & 3\end{array}\right] $
C) $ \left[\begin{array}{rr|r}0 & 1 & 5 \ -1 & 1 & 3\end{array}\right] $
D) $ \left[\begin{array}{ll|l}1 & 0 & 2 \ 0 & 1 & 5\end{array}\right] $

Accepted Answer

Adding $ R_{1} $ to $ R_{2} $ results in the second row becoming $0, 1, 5$, which matches option D.

Question 20

Use a graphing calculator to find the matrix product and/or sum.
-$$
\mathrm{A}=\left[\begin{array}{rrrr}
11 & 14 & 18 & 18 \
30 & 5 & 7 & 2 \
11 & 3 & 2 & 1 \
5 & 32 & 5 & 19
\end{array}\right] \mathrm{B}=\left[\begin{array}{rrr}
12 & 5 & 3 \
18 & 8 & 12 \
7 & 4 & 2 \
21 & 15 & 0
\end{array}\right]
$$
A) $ \left[\begin{array}{rrr}888 & 509 & 237 \ 541 & 248 & 164 \ 221 & 102 & 73 \ 1070 & 586 & 409\end{array}\right] $
B) $ \left[\begin{array}{rrr}732 & 305 & 113 \ 792 & 352 & 528 \ 119 & 68 & 34 \ 1281 & 915 & 0\end{array}\right] $
C)
$ \left[\begin{array}{rrrr}220 & 280 & 360 & 360 \ 1140 & 190 & 266 & 76 \ 143 & 39 & 26 & 13 \ 180 & 1152 & 180 & 684\end{array}\right] $
D) Does not exist

Accepted Answer

The answer of Use a graphing calculator to find the...

Quiz 2: Systems of Linear Equations and Matrices

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. - $2.6 x-0.7 y+5.3 z-3.4 w=12.9$ $6.5 \mathrm{y} \quad+0.7 \mathrm{w}=-1.8$ $4.0 z-2.2 w=1.5$ $4.9 x+0.6 w=3.2$

Use the Gauss-Jordan method to solve the system of equations. - $5 x-3 y=6$ $25 x-15 y=9$

Find the ratios of products A, B, and C using a closed model. -

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - $\begin{array}{l}3 x+y=15 \\2 x+4 y=0\end{array}$

Find the production matrix for the input-output and demand matrices using the open model. - $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$

Solve the problem. -Suppose the following matrix represents the input-output matrix, T, of a simplified economy. Find the amount of each commodity that should be produced.

-

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}x-y+z=-7 \\x+y+z=1 \\x+y-z=-1\end{array}$

Find the ratios of products A, B, and C using a closed model. -

- AB is a 2 × 2 matrix.

Use a graphing calculator to find the matrix product and/or sum. -Find $\mathrm{AB}$ . $A=\left[\begin{array}{rrrr}18 & 14 & 18 & 18 \\30 & 5 & 7 & 2 \\11 & 3 & 2 & 1 \\5 & 32 & 5 & 7\end{array}\right] B=\left[\begin{array}{rrr}18 & 5 & 3 \\18 & 8 & 12 \\7 & 4 & 2 \\21 & 15 & 13\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}x-y+z=4 \\x+y+z=-2 \\x+y-z=-12\end{array}$

For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. - $\begin{array}{r}x+3 y+4 z=80 \\4 y+5 z=40\end{array}$

Find the ratios of products A, B, and C using a closed model. -

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}9 x-2 y+5 z=78 \\2 x+3 y-9 z=-50 \\3 x-8 y+6 z=49\end{array}$

Provide an appropriate response. -True or False?

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ . $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$

Use a graphing calculator to find the matrix product and/or sum. - $\mathrm{A}=\left[\begin{array}{rrrr}11 & 14 & 18 & 18 \\30 & 5 & 7 & 2 \\11 & 3 & 2 & 1 \\5 & 32 & 5 & 19\end{array}\right] \mathrm{B}=\left[\begin{array}{rrr}12 & 5 & 3 \\18 & 8 & 12 \\7 & 4 & 2 \\21 & 15 & 0\end{array}\right]$

Quiz 2: Systems of Linear Equations and Matrices

Use the Gauss-Jordan method to solve the system of equations. - 5x−3y=65 x-3 y=65x−3y=6 25x−15y=9 25 x-15 y=9 25x−15y=9

Find the ratios of products A, B, and C using a closed model. -

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - 3x+y=152x+4y=0\begin{array}{l}3 x+y=15 \\2 x+4 y=0\end{array}3x+y=152x+4y=0​

Find the production matrix for the input-output and demand matrices using the open model. - A=[0.20.10.50.4],D=[36]A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]A=[0.20.5​0.10.4​],D=[36​]

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers J and K. What is The cost of 100 batches of each candy using ingredients from supplier K?

Solve the problem. -Suppose the following matrix represents the input-output matrix, T, of a simplified economy. Find the amount of each commodity that should be produced.

-

Solve the system of equations by using the inverse of the coefficient matrix. - x−y+z=−7x+y+z=1x+y−z=−1\begin{array}{l}x-y+z=-7 \\x+y+z=1 \\x+y-z=-1\end{array}x−y+z=−7x+y+z=1x+y−z=−1​

Find the ratios of products A, B, and C using a closed model. -

- AB is a 2 × 2 matrix.

Use the Gauss-Jordan method to solve the system of equations. - x−y+z=4x+y+z=−2x+y−z=−12\begin{array}{l}x-y+z=4 \\x+y+z=-2 \\x+y-z=-12\end{array}x−y+z=4x+y+z=−2x+y−z=−12​

For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. - x+3y+4z=804y+5z=40\begin{array}{r}x+3 y+4 z=80 \\4 y+5 z=40\end{array}x+3y+4z=804y+5z=40​

Find the inverse, if it exists, for the matrix. -

Find the ratios of products A, B, and C using a closed model. -

Solve the system of equations by using the inverse of the coefficient matrix. - 9x−2y+5z=782x+3y−9z=−503x−8y+6z=49\begin{array}{l}9 x-2 y+5 z=78 \\2 x+3 y-9 z=-50 \\3 x-8 y+6 z=49\end{array}9x−2y+5z=782x+3y−9z=−503x−8y+6z=49​

Provide an appropriate response. -True or False?

Use the indicated row operation to change the matrix. -Replace R2 R_{2} R2​ by R1+R2 R_{1}+R_{2} R1​+R2​ . [102−113] \left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right] [1−1​01​23​]

Use the Gauss-Jordan method to solve the system of equations. - $5 x-3 y=6$ $25 x-15 y=9$

Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the inverse doesn't exist. - $\begin{array}{l}3 x+y=15 \\2 x+4 y=0\end{array}$

Find the production matrix for the input-output and demand matrices using the open model. - $A=\left[\begin{array}{ll}0.2 & 0.1 \\0.5 & 0.4\end{array}\right], D=\left[\begin{array}{l}3 \\6\end{array}\right]$

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}x-y+z=-7 \\x+y+z=1 \\x+y-z=-1\end{array}$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}x-y+z=4 \\x+y+z=-2 \\x+y-z=-12\end{array}$

For the following systems of equations in echelon form, tell how many solutions there are in nonnegative integers. - $\begin{array}{r}x+3 y+4 z=80 \\4 y+5 z=40\end{array}$

Solve the system of equations by using the inverse of the coefficient matrix. - $\begin{array}{l}9 x-2 y+5 z=78 \\2 x+3 y-9 z=-50 \\3 x-8 y+6 z=49\end{array}$

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $R_{1}+R_{2}$ . $\left[\begin{array}{rr|r}1 & 0 & 2 \\ -1 & 1 & 3\end{array}\right]$