Question 1

Find the matrix product, if possible.
-$ \left[\begin{array}{rr}3 & -1 \ 3 & 0\end{array}\right]\left[\begin{array}{rr}0 & -1 \ 3 & 6\end{array}\right] $

Accepted Answer

A)  $ \left[\begin{array}{ll}0 & 1 \ 9 & 0\end{array}\right] $ 
B)  $ \left[\begin{array}{rr}-3 & -9 \ 0 & -3\end{array}\right] $ 
C)  $ \left[\begin{array}{rr}-3 & 0 \ 27 & -3\end{array}\right] $ 
D)  $ \left[\begin{array}{rr}-9 & -3 \ -3 & 0\end{array}\right] $

Question 2

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

Accepted Answer

A)  $ 33: 24: 10 $ 
B)  $ 55: 76: 23 $ 
C)  $ 2: 3: 3 $ 
D)  $ 8: 11: 10 $

Question 3

Use graphing calculator to find the inverse of the matrix. Give 5 decimal places.
-$$
A=\left[\begin{array}{lll}
1.52 & 5.55 & 4 \
-0.63 & 7.33 & 3.21 \
8.2 & 0.003 & -2.8
\end{array}\right]
$$

Accepted Answer

A)  $ \left[\begin{array}{lll}0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0\end{array}\right] $ 
B)  $ \left[\begin{array}{rlr}0.65789 & 0.18018 & 0.25 \ -1.58730 & 0.13643 & 0.31153 \ 0.12195 & 333.33333 & -0.35714\end{array}\right] $ 
C)  $ \left[\begin{array}{rrr}0.02137 & -0.01623 & 0.01192 \ -0.27464 & 0.34436 & 0.00245 \ 0.62294 & -0.47163 & -0.00792\end{array}\right] $ 
D)  $ \left[\begin{array}{rrr}0.15171 & -0.11491 & 0.08500 \ -0.18145 & 0.27379 & 0.05467 \ 0.44411 & -0.33622 & -0.10815\end{array}\right] $

Question 4

Use the Gauss-Jordan method to solve the system of equations.
-$$
\begin{array}{l}
6 x+5 y=0 \
3 x+9 y=39
\end{array}
$$

Accepted Answer

A)  $ (-5,-6) $ 
B)  $ (6,-5) $ 
C)  $ (-5,6) $ 
D)  No solution

Question 5

Use the Gauss-Jordan method to solve the system of equations.$$
\begin{array}{l}
3 x-2 y=-3 \
9 x-6 y=-9
\end{array}
$$

Accepted Answer

A)  $ (1,3) $ 
B)  $ \left(-1-\frac{2}{3} y, y\right) $ 
C)  $ \left(-1+\frac{2}{3} y, y\right) $ 
D)  No solution

Question 6

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

Accepted Answer

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

Question 7

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.
-$$
\begin{array}{l}
3 x-6 y=-3 \
6 x-12 y=-9
\end{array}
$$

Accepted Answer

A)  No inverse, no solution for system 
B)  $ (2,2) $ 
C)  $ (-3,-9) $ 
D)  No inverse, $ \left(-1-\frac{1}{2} y, y\right) $

Question 8

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these
products exist.
-$ A $ is $ 2 \times 2 $, and $ B $ is $ 2 \times 2 $.

Accepted Answer

A)  $ 4 \times 2 ; 4 \times 2 $ 
B)  $ 2 \times 2 ; 2 \times 2 $ 
C)  $ 2 \times 4 ; 2 \times 4 $ 
D)  $ 1 \times 1 ; 1 \times 1 $

Question 9

Provide an appropriate response.
-True or False?

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-Anne and Nancy use a metal alloy that is 25.75% copper to make jewelry. How many ounces of a 19% alloy must be mixed with a 28% alloy to form 92 ounces of the desired alloy?

Accepted Answer

A) 25 ounces 
B) 23 ounces 
C) 74 ounces 
D) 69 ounces

Question 11

Write the system of equations associated with the augmented matrix.
-$ \left[\begin{array}{rr|r}1 & 0 & 2 \ 0 & 1 & -3\end{array}\right] $

Accepted Answer

A)  $ x=1 $
$ y=1 $ 
B)  $ x=-2 $
$ \mathrm{y}=3 $ 
C)  $ x=0 $
$ y=0 $ 
D)  $ x=2 $
$ \mathrm{y}=-3 $

Question 12

Decide whether the matrices are inverses of each other. (Check to see if their product is the identity matrix I.)
-$ \left[\begin{array}{rrr}1 & 2 & 0 \ -2 & 0 & 2 \ 3 & 2 & -4\end{array}\right] $ and $ \left[\begin{array}{rrr}\frac{1}{2} & -1 & -\frac{1}{2} \ \frac{1}{4} & \frac{1}{2} & \frac{1}{4} \ \frac{1}{2} & -\frac{1}{2} & -\frac{1}{2}\end{array}\right] $

Accepted Answer

A) True 
 B)False

Question 13

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $$
2.7 x-0.2 y-5.0 z=2.6
$$
$ 5.6 x+4.6 y-0.5 z=-4.1 $
$ 3.4 x-1.3 y+1.6 z=10.5 $

Accepted Answer

A)  $ (1.7,-2.9,0.5) $ 
B)  $ (8.6,-14.6,2.6) $ 
C)  $ (6.9,-11.7,2.1) $ 
D)  $ (3.4,-5.9,1.1) $

Question 14

Decide whether the matrices are inverses of each other. (Check to see if their product is the identity matrix I.) $ \left.\begin{array}{rr}-2 & 4 \ 4 & -4\end{array}\right] $ and $ \left[\begin{array}{ll}\frac{1}{2} & \frac{1}{4} \ \frac{1}{2} & \frac{1}{4}\end{array}\right] $

Accepted Answer

A) True 
 B)False

Question 15

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 X? 
$$
A=\left[\begin{array}{ccc}
\text { sugar choc milk } \
4 & 6 & 1 \
5 & 3 & 1 \
3 & 3 & 1
\end{array}\right] \text { cherry }
$$
$$
B=\left[\begin{array}{ll}
X & Y \
3 & 2 \
3 & 4 \
2 & 2
\end{array}\right] \text { sugar }
$$

Accepted Answer

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

Question 16

Solve the system of equations. Let z be the parameter.
-$
7 x+3 y+5 z=-20
$
$ 3 x+y+2 z=2 $

Accepted Answer

A)  $ \left(13-\frac{1}{2} z, 2+2 z, z\right) $ 
B)  $ (-26+z, 74+z, z) $ 
C)  $ \left(13-\frac{1}{2} z,-37-\frac{1}{2} z, z\right) $ 
D)  $ \left(13-\frac{1}{2} z, 2-2 z, z\right) $

Question 17

Provide an appropriate response
-Which choice best describes the following matrix? $$
\left[\begin{array}{l}
24 \
25 \
20 \
17 \
18
\end{array}\right]
$$

Accepted Answer

A)  Column matrix 
B)  Row matrix 
C)  Square matrix 
D)  $ 1 \times 5 $ matrix

Question 18

Decide whether the matrices are inverses of each other. (Check to see if their product is the identity matrix I.)$ \left[\begin{array}{rr}-5 & -1 \ 6 & 0\end{array}\right] $ and $ \left[\begin{array}{cc}0 & \frac{1}{6} \ -1 & \frac{5}{6}\end{array}\right] $

Accepted Answer

A) True 
 B)False

Question 19

Solve the problem.
-Mike, Joe, and Bill are painting a fence. The painting can be finished if Mike and Joe work together for 4 hours and Bill works alone for 2 hours; or if Mike and Joe work together for 2 hours and Bill Works alone for 5 hours; or if Mike works alone for 6 hours, Joe works alone for 2 hours, and Bill Works alone for 1 hour. How much time does it take for each man working alone to complete the Painting?

Accepted Answer

A) Mike: 12 hr; Joe: 10 hr; Bill: 10 hr 
B) Mike: 8 hr; Joe: 8 hr; Bill: 16 hr 
C) Mike: 16 hr; Joe: 8 hr; Bill: 8 hr 
D) Mike: 8 hr; Joe: 16 hr; Bill: 8 hr

Question 20

Use the Gauss-Jordan method to solve the system of equations.$ 8 w+8 x-6 y-2 z=-30 $
$ 7 w+6 x-9 y-2 z=-38 $
$ 8 w+8 x+7 y+3 z=17 $
$ -6 w-2 x+8 y+8 z=18 $

Accepted Answer

A)   (-1,4,-5,2) 
B)  (2,3,-4,-2) 
C)  (2,-3,4,-1) 
D)  No solution

Exam 2: Systems of Linear Equations and Matrices

Find the matrix product, if possible. - $\left[\begin{array}{rr}3 & -1 \\ 3 & 0\end{array}\right]\left[\begin{array}{rr}0 & -1 \\ 3 & 6\end{array}\right]$

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

Use graphing calculator to find the inverse of the matrix. Give 5 decimal places. - $A=\left[\begin{array}{lll}1.52 & 5.55 & 4 \\-0.63 & 7.33 & 3.21 \\8.2 & 0.003 & -2.8\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}6 x+5 y=0 \\3 x+9 y=39\end{array}$

Use the Gauss-Jordan method to solve the system of equations. $\begin{array}{l}3 x-2 y=-3 \\9 x-6 y=-9\end{array}$

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. - $\begin{array}{l}3 x-6 y=-3 \\6 x-12 y=-9\end{array}$

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist. - $A$ is $2 \times 2$ , and $B$ is $2 \times 2$ .

Provide an appropriate response. -True or False?

Solve the problem. -Anne and Nancy use a metal alloy that is 25.75% copper to make jewelry. How many ounces of a 19% alloy must be mixed with a 28% alloy to form 92 ounces of the desired alloy?

Write the system of equations associated with the augmented matrix. - $\left[\begin{array}{rr|r}1 & 0 & 2 \\ 0 & 1 & -3\end{array}\right]$

Use a graphing calculator to solve the system of equations. Round your solution to one decimal place. $2.7 x-0.2 y-5.0 z=2.6$ $5.6 x+4.6 y-0.5 z=-4.1$ $3.4 x-1.3 y+1.6 z=10.5$

Decide whether the matrices are inverses of each other. (Check to see if their product is the identity matrix I.) $\left.\begin{array}{rr}-2 & 4 \\ 4 & -4\end{array}\right]$ and $\left[\begin{array}{ll}\frac{1}{2} & \frac{1}{4} \\ \frac{1}{2} & \frac{1}{4}\end{array}\right]$

Solve the system of equations. Let z be the parameter. - $7 x+3 y+5 z=-20$ $3 x+y+2 z=2$

Provide an appropriate response -Which choice best describes the following matrix? $\left[\begin{array}{l}24 \\25 \\20 \\17 \\18\end{array}\right]$

Decide whether the matrices are inverses of each other. (Check to see if their product is the identity matrix I.) $\left[\begin{array}{rr}-5 & -1 \\ 6 & 0\end{array}\right]$ and $\left[\begin{array}{cc}0 & \frac{1}{6} \\ -1 & \frac{5}{6}\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. $8 w+8 x-6 y-2 z=-30$ $7 w+6 x-9 y-2 z=-38$ $8 w+8 x+7 y+3 z=17$ $-6 w-2 x+8 y+8 z=18$

Exam 2: Systems of Linear Equations and Matrices

Find the matrix product, if possible. - [3−130][0−136] \left[\begin{array}{rr}3 & -1 \\ 3 & 0\end{array}\right]\left[\begin{array}{rr}0 & -1 \\ 3 & 6\end{array}\right] [33​−10​][03​−16​]

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

Use graphing calculator to find the inverse of the matrix. Give 5 decimal places. - A=[1.525.554−0.637.333.218.20.003−2.8]A=\left[\begin{array}{lll}1.52 & 5.55 & 4 \\-0.63 & 7.33 & 3.21 \\8.2 & 0.003 & -2.8\end{array}\right]A=​1.52−0.638.2​5.557.330.003​43.21−2.8​​

Use the Gauss-Jordan method to solve the system of equations. - 6x+5y=03x+9y=39\begin{array}{l}6 x+5 y=0 \\3 x+9 y=39\end{array}6x+5y=03x+9y=39​

Use the Gauss-Jordan method to solve the system of equations. 3x−2y=−39x−6y=−9\begin{array}{l}3 x-2 y=-3 \\9 x-6 y=-9\end{array}3x−2y=−39x−6y=−9​

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

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−6y=−36x−12y=−9\begin{array}{l}3 x-6 y=-3 \\6 x-12 y=-9\end{array}3x−6y=−36x−12y=−9​

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist. - A A A is 2×2 2 \times 2 2×2 , and B B B is 2×2 2 \times 2 2×2 .

Provide an appropriate response. -True or False?

Solve the problem. -Anne and Nancy use a metal alloy that is 25.75% copper to make jewelry. How many ounces of a 19% alloy must be mixed with a 28% alloy to form 92 ounces of the desired alloy?

Write the system of equations associated with the augmented matrix. - [10201−3] \left[\begin{array}{rr|r}1 & 0 & 2 \\ 0 & 1 & -3\end{array}\right] [10​01​2−3​]

Solve the system of equations. Let z be the parameter. - 7x+3y+5z=−207 x+3 y+5 z=-207x+3y+5z=−20 3x+y+2z=2 3 x+y+2 z=2 3x+y+2z=2

Provide an appropriate response -Which choice best describes the following matrix? [2425201718]\left[\begin{array}{l}24 \\25 \\20 \\17 \\18\end{array}\right]​2425201718​​

Use the Gauss-Jordan method to solve the system of equations. 8w+8x−6y−2z=−30 8 w+8 x-6 y-2 z=-30 8w+8x−6y−2z=−30 7w+6x−9y−2z=−38 7 w+6 x-9 y-2 z=-38 7w+6x−9y−2z=−38 8w+8x+7y+3z=17 8 w+8 x+7 y+3 z=17 8w+8x+7y+3z=17 −6w−2x+8y+8z=18 -6 w-2 x+8 y+8 z=18 −6w−2x+8y+8z=18

Find the matrix product, if possible. - $\left[\begin{array}{rr}3 & -1 \\ 3 & 0\end{array}\right]\left[\begin{array}{rr}0 & -1 \\ 3 & 6\end{array}\right]$

Use graphing calculator to find the inverse of the matrix. Give 5 decimal places. - $A=\left[\begin{array}{lll}1.52 & 5.55 & 4 \\-0.63 & 7.33 & 3.21 \\8.2 & 0.003 & -2.8\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. - $\begin{array}{l}6 x+5 y=0 \\3 x+9 y=39\end{array}$

Use the Gauss-Jordan method to solve the system of equations. $\begin{array}{l}3 x-2 y=-3 \\9 x-6 y=-9\end{array}$

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. - $\begin{array}{l}3 x-6 y=-3 \\6 x-12 y=-9\end{array}$

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these products exist. - $A$ is $2 \times 2$ , and $B$ is $2 \times 2$ .

Write the system of equations associated with the augmented matrix. - $\left[\begin{array}{rr|r}1 & 0 & 2 \\ 0 & 1 & -3\end{array}\right]$

Solve the system of equations. Let z be the parameter. - $7 x+3 y+5 z=-20$ $3 x+y+2 z=2$

Provide an appropriate response -Which choice best describes the following matrix? $\left[\begin{array}{l}24 \\25 \\20 \\17 \\18\end{array}\right]$

Use the Gauss-Jordan method to solve the system of equations. $8 w+8 x-6 y-2 z=-30$ $7 w+6 x-9 y-2 z=-38$ $8 w+8 x+7 y+3 z=17$ $-6 w-2 x+8 y+8 z=18$