Question 1

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $ \left[\begin{array}{rr}9 & -2 \ 7 & -2\end{array}\right] $ and $ \left[\begin{array}{rr}\frac{1}{2} & \frac{1}{2} \ -\frac{7}{4} & -\frac{9}{4}\end{array}\right] $

Accepted Answer

A) True 
 B)False

Question 2

Find the matrix product, if possible.
-$ \left[\begin{array}{rrr}3 & -2 & 1 \ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \ -2 & 1\end{array}\right] $

Accepted Answer

A)  $ \left[\begin{array}{rr}9 & -6 \ -6 & 8 \ 3 & -5\end{array}\right] $ 
B)  $ \left[\begin{array}{rrr}9 & -6 & 3 \ -6 & 8 & -5\end{array}\right] $ 
C)  $ \left[\begin{array}{ll}9 & 0 \ 0 & 4\end{array}\right] $ 
D)  Does not exist

Question 3

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] $

Accepted Answer

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] $

Question 4

Provide an appropriate response.
-If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

Accepted Answer

A) K is a 2 × 5 matrix and each of its entries is the negative of the corresponding entry of A. 
B) K is a 2 × 5 matrix and all entries of K are equal to 0. 
C) K is a 5 × 2 matrix and all entries of K are equal to 0. 
D) K is a 5 × 2 matrix and each of its entries is the negative of the corresponding entry of A.

Question 5

Use the indicated row operation to change the matrix.
-Replace $ R_{2} $ by $ \frac{1}{3} R_{1}+\frac{1}{2} R_{2} $.
$ \left[\begin{array}{rr|r}3 & 0 & 15 \ -2 & 4 & 12\end{array}\right] $

Accepted Answer

A)  $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 0 & 2 & 11\end{array}\right] $ 
B)  $ \left[\begin{array}{rr|r}3 & 0 & 15 \ -1 & 2 & 6\end{array}\right] $ 
C)  $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 1 & 4 & 27\end{array}\right] $ 
D)  $ \left[\begin{array}{ll|l}3 & 0 & 15 \ 0 & 0 & 11\end{array}\right] $

Question 6

Solve the problem.
-Janet is planning to visit Arizona, New Mexico, and California on a 20-day vacation. If she plans to spend as much time in New Mexico as she does in the other two states combined, how can she allot her time in the three states? (Let $ x $ denote the number of days in Arizona, $ y $ the number of days in New Mexico, and $ z $ the number of days in California. Let $ z $ be the parameter.)

Accepted Answer

A)  $ x=10, y=10-z, 0 \leq z \leq 10 $ 
B)  $ x=10, y=z-10,0 \leq z \leq 10 $ 
C)  $ x=z-10, y=10,0 \leq z \leq 10 $ 
D)  $ x=10-z, y=10,0 \leq z \leq 10 $

Question 7

Use the Gauss-Jordan method to solve the system of equations.
-$
\begin{array}{l}
8 x+9 y-z=48 \
x-4 y+7 z=65 \
2 x+y+z=22
\end{array}
$

Accepted Answer

A)  $ (6,1,9) $ 
B)  $ (6,9,1) $ 
C)  $ (-6,1,12) $ 
D)  No solution

Question 8

The property does not apply to matrix multiplication.

Accepted Answer

The answer of The property does not apply to matrix...

Question 9

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 X and Y. What is The cost of 100 batches of each candy using ingredients from supplier Y?

Accepted Answer

A)  $ \$ 6600 $ 
B)  $ \$ 7800 $ 
C)  $ \$ 3300 $ 
D)  $ \$ 4800 $

Question 10

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

Accepted Answer

A)  $ (-4,1,4) $ 
B)  $ (1,-4,4) $ 
C)  $ (-4,4,1) $ 
D)  No inverse, no solution for system

Question 11

Find the value.
-Let $ \mathrm{C}=\left[\begin{array}{r}6 \ -2 \ 12\end{array}\right] ; \frac{1}{2} \mathrm{C} $

Accepted Answer

A)  $ \left[\begin{array}{r}3 \ -2 \ 12\end{array}\right] $ 
B)  $ \left[\begin{array}{r}6 \ -1 \ 12\end{array}\right] $ 
C)  $ \left[\begin{array}{r}3 \ -1 \ 6\end{array}\right] $ 
D)  $ \left[\begin{array}{r}12 \ -4 \ 24\end{array}\right] $

Question 12

Find the inverse, if it exists, for the matrix.
-$$
A=\left[\begin{array}{rrrr}
2 & -3 & 0 & 2 \
6 & -6 & 0 & 4 \
6 & -12 & 0 & 6 \
0 & 0 & -2 & 0
\end{array}\right]
$$

Accepted Answer

A) 
$$
\left[\begin{array}{cccc}
\frac{1}{2} & -\frac{1}{3} & 0 & \frac{1}{2} \
\frac{1}{6} & -\frac{1}{6} & 0 & \frac{1}{4} \
\frac{1}{6} & -\frac{1}{12} & 0 & \frac{1}{6} \
0 & 0 & -\frac{1}{2} & 0
\end{array}\right] 
B)  
\left[\begin{array}{cccc}
-1 & 1 & 0 & 3 \
\frac{1}{2} & 0 & 0 & -\frac{1}{2} \
0 & -\frac{1}{3} & 0 & -\frac{1}{2} \
0 & 0 & -\frac{1}{2} & 0
\end{array}\right]
$$ 
C) $$
\left[\begin{array}{cccc}
-1 & \frac{1}{2} & 0 & 0 \
1 & 0 & -\frac{1}{3} & 0 \
0 & 0 & 0 & -\frac{1}{2} \
3-\frac{1}{2} & -\frac{1}{2} & 0
\end{array}\right]
$$ 
D)  No inverse

Question 13

Accepted Answer

The answer of ...

Question 14

Perform the indicated operation, where possible.
-$
\left[\begin{array}{lll}
2 & 4
\end{array}\right]+\left[\begin{array}{c}
-4 \
9
\end{array}\right]
$

Accepted Answer

A)  $ \left[\begin{array}{ll}-2 & 13\end{array}\right] $ 
B)  $ \left[\begin{array}{c}-2 \ 13\end{array}\right] $ 
C)  $ \left[\begin{array}{rr}2 & -4 \ 4 & 9\end{array}\right] $ 
D)  Not possible

Question 15

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place.$$
\begin{array}{l}
1.5 x-0.4 y+1.6 z=2.4 \
4.5 x-7.0 y-0.4 z=-4.0 \
3.8 x+2.4 y+2.0 z=8.6
\end{array}
$$

Accepted Answer

A)  $ (0.8,0.9,0.6) $ 
B)  $ (1.1,1.2,0.8) $ 
C)  $ (0.5,0.6,0.4) $ 
D)  $ (0.3,0.3,0.2) $

Question 16

-

Accepted Answer

A) True 
 B)False

Question 17

Use the Gauss-Jordan method to solve the system of equations.
-$$
\begin{array}{l}
x+y+z=7 \
x-y+2 z=7 \
2 x+3 z=14
\end{array}
$$

Accepted Answer

A)  $ \left(\frac{-3 z+14}{2}, \frac{z}{2}, z\right) $ 
B)  $ \left(\frac{-3 z-14}{2}, \frac{z}{2}, z\right) $ 
C)  $ \left(\frac{-3 z+14}{2}, 2 z, z\right) $ 
D)  $ \left(\frac{3 z+14}{2}, \frac{z}{2}, z\right) $

Question 18

Use the echelon method to solve the system of two equations in two unknowns.
-$$
\begin{array}{l}
4 x-2 y=9 \
20 x-10 y=27
\end{array}
$$

Accepted Answer

A)  $ \left(\frac{1}{2} y+\frac{9}{4}, y\right) $ 
B)  $ \left(1,-\frac{5}{2}\right) $ 
C)  $ (1,0) $ 
D)  No solution

Question 19

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

Accepted Answer

A)  13: 25: 100 
B)  $ 33: 67: 63 $ 
C)  1: $ 149: 100 $ 
D)  1: 25: 25

Question 20

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

Accepted Answer

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] $

Exam 2: Systems of Linear Equations and Matrices

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $\left[\begin{array}{rr}9 & -2 \\ 7 & -2\end{array}\right]$ and $\left[\begin{array}{rr}\frac{1}{2} & \frac{1}{2} \\ -\frac{7}{4} & -\frac{9}{4}\end{array}\right]$

Find the matrix product, if possible. - $\left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right]$

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

Provide an appropriate response. -If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

Use the indicated row operation to change the matrix. -Replace $R_{2}$ by $\frac{1}{3} R_{1}+\frac{1}{2} R_{2}$ . $\left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}8 x+9 y-z=48 \\x-4 y+7 z=65 \\2 x+y+z=22\end{array}$

The property does not apply to matrix multiplication.

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 value. -Let $\mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C}$

Find the inverse, if it exists, for the matrix. - $A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$

Perform the indicated operation, where possible. - $\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right]$

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $\begin{array}{l}1.5 x-0.4 y+1.6 z=2.4 \\4.5 x-7.0 y-0.4 z=-4.0 \\3.8 x+2.4 y+2.0 z=8.6\end{array}$

-

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}x+y+z=7 \\x-y+2 z=7 \\2 x+3 z=14\end{array}$

Use the echelon method to solve the system of two equations in two unknowns. - $\begin{array}{l}4 x-2 y=9 \\20 x-10 y=27\end{array}$

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

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

Exam 2: Systems of Linear Equations and Matrices

Find the matrix product, if possible. - [3−2104−3][30−21] \left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right] [30​−24​1−3​][3−2​01​]

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​]

Provide an appropriate response. -If A is a 5 × 2 matrix and A+ K = A, what can you say about K?

Use the indicated row operation to change the matrix. -Replace R2 R_{2} R2​ by 13R1+12R2 \frac{1}{3} R_{1}+\frac{1}{2} R_{2} 31​R1​+21​R2​ . [3015−2412] \left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right] [3−2​04​1512​]

Use the Gauss-Jordan method to solve the system of equations. - 8x+9y−z=48x−4y+7z=652x+y+z=22\begin{array}{l}8 x+9 y-z=48 \\x-4 y+7 z=65 \\2 x+y+z=22\end{array}8x+9y−z=48x−4y+7z=652x+y+z=22​

The property does not apply to matrix multiplication.

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 X and Y. What is The cost of 100 batches of each candy using ingredients from supplier Y?

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 value. -Let C=[6−212];12C \mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C} C=​6−212​​;21​C

Find the inverse, if it exists, for the matrix. - A=[2−3026−6046−120600−20]A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]A=​2660​−3−6−120​000−2​2460​​

Perform the indicated operation, where possible. - [24]+[−49]\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right][2​4​]+[−49​]

-

Use the Gauss-Jordan method to solve the system of equations. - x+y+z=7x−y+2z=72x+3z=14\begin{array}{l}x+y+z=7 \\x-y+2 z=7 \\2 x+3 z=14\end{array}x+y+z=7x−y+2z=72x+3z=14​

Use the echelon method to solve the system of two equations in two unknowns. - 4x−2y=920x−10y=27\begin{array}{l}4 x-2 y=9 \\20 x-10 y=27\end{array}4x−2y=920x−10y=27​

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

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​]

Find the matrix product, if possible. - $\left[\begin{array}{rrr}3 & -2 & 1 \\ 0 & 4 & -3\end{array}\right]\left[\begin{array}{rr}3 & 0 \\ -2 & 1\end{array}\right]$

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 the indicated row operation to change the matrix. -Replace $R_{2}$ by $\frac{1}{3} R_{1}+\frac{1}{2} R_{2}$ . $\left[\begin{array}{rr|r}3 & 0 & 15 \\ -2 & 4 & 12\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}8 x+9 y-z=48 \\x-4 y+7 z=65 \\2 x+y+z=22\end{array}$

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 value. -Let $\mathrm{C}=\left[\begin{array}{r}6 \\ -2 \\ 12\end{array}\right] ; \frac{1}{2} \mathrm{C}$

Find the inverse, if it exists, for the matrix. - $A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$

Perform the indicated operation, where possible. - $\left[\begin{array}{lll}2 & 4\end{array}\right]+\left[\begin{array}{c}-4 \\9\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}x+y+z=7 \\x-y+2 z=7 \\2 x+3 z=14\end{array}$

Use the echelon method to solve the system of two equations in two unknowns. - $\begin{array}{l}4 x-2 y=9 \\20 x-10 y=27\end{array}$

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