Question 1

Write the augmented matrix for the system of linear equations. $$\left\{ \begin{aligned}
x - 3 y - 2 z & = - 2 \
4 y + 4 z & = 4 \
x + 4 z & = - 2
\end{aligned} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
0 & 4 & 4 & \vdots & 4 \
1 & 4 & 0 & \vdots & - 2
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
4 & 44 & 0 & \vdots & 4 \
1 & 4 & 0 & \vdots & - 2
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
1 & 4 & 4 & \vdots & 4 \
1 & 1 & 4 & \vdots & - 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
& 4 & 4 & \vdots & 4 \
1 & & 4 & \vdots & - 2
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
0 & 4 & 4 & \vdots & 4 \
1 & 0 & 4 & \vdots & - 2
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
0 & 4 & 4 & \vdots & 4 \
1 & 4 & 0 & \vdots & - 2
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
4 & 44 & 0 & \vdots & 4 \
1 & 4 & 0 & \vdots & - 2
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
1 & 4 & 4 & \vdots & 4 \
1 & 1 & 4 & \vdots & - 2
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
& 4 & 4 & \vdots & 4 \
1 & & 4 & \vdots & - 2
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c c c c } 
1 & - 3 & - 2 & \vdots & - 2 \
0 & 4 & 4 & \vdots & 4 \
1 & 0 & 4 & \vdots & - 2
\end{array} \right]$

Question 2

Find 3A - 2B.  $$A = \left[ \begin{array} { c c } 
6 & - 4 \
4 & 4 \
- 4 & 4
\end{array} \right] , B = \left[ \begin{array} { c c } 
3 & 4 \
- 1 & - 6 \
2 & 10
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 
14 & - 20 \
14 & - 8 \
- 16 & 24
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
12 & - 20 \
14 & 24 \
- 16 & - 8
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
10 & 24 \
14 & - 20 \
- 16 & - 8
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
8 & - 20 \
24 & 14 \
- 16 & - 8
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
16 & - 20 \
- 16 & 24 \
14 & - 8
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 
14 & - 20 \
14 & - 8 \
- 16 & 24
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
12 & - 20 \
14 & 24 \
- 16 & - 8
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
10 & 24 \
14 & - 20 \
- 16 & - 8
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
8 & - 20 \
24 & 14 \
- 16 & - 8
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
16 & - 20 \
- 16 & 24 \
14 & - 8
\end{array} \right]$

Question 3

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 aij 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%.

Accepted Answer

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

Question 4

Fill in the blank(s) using elementary row operations to form a row-equivalent matrix.  
  $$\left[ \begin{array} { c c c } 
6 & 9 & 4 \
5 & - 4 & 7
\end{array} \right]$$   $$\left[ \begin{array} { c c c } 
2 & \cdots & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$$

Accepted Answer

A)   $\left[ \begin{array} { c c c } 
2 & 9 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
2 & 2 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
C)   $\left[ \begin{array} { l l l } 
2 & - 3 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
2 & 5 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
2 & 3 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
A)   $\left[ \begin{array} { c c c } 
2 & 9 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
2 & 2 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
C)   $\left[ \begin{array} { l l l } 
2 & - 3 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
2 & 5 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
2 & 3 & \frac { 4 } { 3 } \
5 & - 4 & 7
\end{array} \right]$

Question 5

Use the matrix capabilities of a graphing utility to evaluate the expression.Round your results to three decimal places, if necessary.   $55 \left( \left[ \begin{array} { c c } 
12 & - 18 \
- 17 & 19
\end{array} \right] + \left[ \begin{array} { c c } 
- 21 & 13 \
15 & 14
\end{array} \right] \right)$

Accepted Answer

A)  $\left[ \begin{array} { c c } 
- 495 & - 275 \
- 110 & 1815
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 
- 493 & - 275 \
1815 & - 110
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
- 491 & 1815 \
- 110 & - 275
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
- 497 & - 110 \
- 275 & 1815
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
- 499 & - 275 \
- 110 & 1815
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 
- 495 & - 275 \
- 110 & 1815
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 
- 493 & - 275 \
1815 & - 110
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
- 491 & 1815 \
- 110 & - 275
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
- 497 & - 110 \
- 275 & 1815
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
- 499 & - 275 \
- 110 & 1815
\end{array} \right]$

Question 6

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  $$\left\{ \begin{array} { l } 
x + 2 y = 6 \
2 x + y = 9
\end{array} \right.$$

Accepted Answer

A)  (1, 4) 
B)  (3, 4) 
C) (1, 12) 
D) (4, 1) 
E) (12, 4) 
A)  (1, 4) 
B)  (3, 4) 
C) (1, 12) 
D) (4, 1) 
E) (12, 4)

Question 7

Evaluate the expression.   $$- 3 \left( \left[ \begin{array} { c c } 
- 6 & 0 \
4 & - 6
\end{array} \right] + \left[ \begin{array} { c c } 
7 & 3 \
- 5 & - 1
\end{array} \right] \right) - 2 \left[ \begin{array} { c c } 
- 11 & - 10 \
14 & 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 
23 & 11 \
- 25 & 11
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
21 & 11 \
11 & - 25
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
19 & 11 \
- 25 & 11
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
17 & - 25 \
11 & 11
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
15 & 11 \
- 25 & 11
\end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 
23 & 11 \
- 25 & 11
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 
21 & 11 \
11 & - 25
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 
19 & 11 \
- 25 & 11
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 
17 & - 25 \
11 & 11
\end{array} \right]$ 
E)  $\left[ \begin{array} { c c } 
15 & 11 \
- 25 & 11
\end{array} \right]$

Question 8

Find the determinant of the matrix.   $\left[ \begin{array} { c c } 
- 5 & 2 \
\frac { 1 } { 2 } & 1
\end{array} \right]$

Accepted Answer

A) -6 
B) -7 
C) -4 
D) -5 
E) -8 
A) -6 
B) -7 
C) -4 
D) -5 
E) -8

Question 9

Use the matrix capabilities of a graphing utility to find AB, if possible. $$A = \left[ \begin{array} { c c c } 
- 7 & - 2 & - 8 \
2 & - 9 & 3 \
- 7 & - 8 & 6
\end{array} \right] , B = \left[ \begin{array} { c c c } 
4 & 4 & 1 \
- 9 & - 5 & 3 \
3 & - 2 & - 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 
- 28 & - 8 & - 8 \
- 18 & 45 & 9 \
- 21 & 16 & - 30
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
14 & - 34 & - 53 \
116 & 59 & - 10 \
26 & 24 & - 1
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
- 34 & 98 & 62 \
- 2 & 47 & 0 \
27 & - 40 & - 61
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
- 34 & - 2 & 27 \
98 & 47 & - 40 \
62 & 0 & - 61
\end{array} \right]$ 
E) not possible 
A)  $\left[ \begin{array} { c c c } 
- 28 & - 8 & - 8 \
- 18 & 45 & 9 \
- 21 & 16 & - 30
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
14 & - 34 & - 53 \
116 & 59 & - 10 \
26 & 24 & - 1
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
- 34 & 98 & 62 \
- 2 & 47 & 0 \
27 & - 40 & - 61
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
- 34 & - 2 & 27 \
98 & 47 & - 40 \
62 & 0 & - 61
\end{array} \right]$ 
E) not possible

Question 10

Use a determinant to determine whether the points $( 1,4 ) , ( - 2,2 )$ and $( 7,8 )$ are collinear.Show all work.
​

Accepted Answer

@#IMG-DLM& ; therefo

Question 11

Fill in the blank(s) using elementary row operations to form a row-equivalent matrix.   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
5 & - 2 & 4
\end{array} \right]$ $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & \cdots & - 1
\end{array} \right]$

Accepted Answer

A)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 3 & - 1
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 0 & - 1
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & - 9 & - 1
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & - 7 & - 1
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 7 & - 1
\end{array} \right]$ 
A)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 3 & - 1
\end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 0 & - 1
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & - 9 & - 1
\end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & - 7 & - 1
\end{array} \right]$ 
E)   $\left[ \begin{array} { c c c } 
1 & 1 & 1 \
0 & 7 & - 1
\end{array} \right]$

Question 12

Use a determinant and the given vertices of a triangle to find the area of the triangle.

Accepted Answer

A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 6 } { 19 }$ 
C) 18 
D) 38 
E) 40 
A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 6 } { 19 }$ 
C) 18 
D) 38 
E) 40

Question 13

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix $$\left[ \begin{array} { c c c } 
0 & 1 & 1 \
- 2 & 1 & 2 \
2 & - 1 & 0
\end{array} \right]$$ .Show all your work.

Accepted Answer

The answer of Find the uncoded 1 × 3 row...

Question 14

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. $$\begin{array} { l } 
\text { Feed \& Weed } & \text { Winterizer } & 17 - 17 - 17 \
A=\left[\begin{array}{l}
17 \
20 \
17
\end{array}\right.&\begin{array}{l}
21 \
15 \
15
\end{array}&\left.\begin{array}{c}
24 \
26 \
28
\end{array}\right] \begin{array} {l } 
 \text {Friday }\
 \text {Saturday }\
 \text {Sunday }\
\end{array}
\end{array}$$ The selling price per bag and the profit per bag for the three types of fertilizer are represented by B (values are in dollars).   $B = \left[ \begin{array} { l l } 
 \text {Selling Price }& \text { Profit }\
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] \begin{array} { c } \
\text { Feed \& Weed } \
\text { Winterizer } \
17 - 17 - 17
\end{array}$ Compute AB and interpret the result.

Accepted Answer

A)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c c } 
671.75 & 68.70 \
643.25 & 64.70 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
B)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
671.75 & 68.70 \
643.25 & 64.70 \
62.50 & 625.25
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
C)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
68.70 & 671.75 \
643.25 & 64.70 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
D)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
68.70 & 671.75 \
64.70 & 643.25 \
62.50 & 625.25
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
E)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
671.75 & 68.70 \
64.70 & 643.25 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
A)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c c } 
671.75 & 68.70 \
643.25 & 64.70 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
B)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
671.75 & 68.70 \
643.25 & 64.70 \
62.50 & 625.25
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
C)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
68.70 & 671.75 \
643.25 & 64.70 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
D)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
68.70 & 671.75 \
64.70 & 643.25 \
62.50 & 625.25
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$ 
E)  Total Total
Revenue Profit
$$A B = \left[ \begin{array} { l l l } 
17 & 21 & 24 \
20 & 15 & 26 \
17 & 15 & 28
\end{array} \right] \left[ \begin{array} { c c } 
11.50 & 1.20 \
13.25 & 1.50 \
8.25 & 0.70
\end{array} \right] = \left[ \begin{array} { c c } 
671.75 & 68.70 \
64.70 & 643.25 \
625.25 & 62.50
\end{array} \right] \begin{array} { c } 
\text { Friday } \
\text { Saturday } \
\text { Sunday }
\end{array}$$

Question 15

Find x and y.   $$\left[ \begin{array} { c c } 
x & - 2 \
7 & y
\end{array} \right] = \left[ \begin{array} { c c } 
- 20 & - 2 \
7 & 3
\end{array} \right]$$

Accepted Answer

A)  $x = 20 , y = - 3$ 
B)  $x = \frac { 1 } { 20 } , y = - \frac { 1 } { 3 }$ 
C)  $x = \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$ 
D)  $x = - 20 , y = 3$ 
E)  $x = - \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$ 
A)  $x = 20 , y = - 3$ 
B)  $x = \frac { 1 } { 20 } , y = - \frac { 1 } { 3 }$ 
C)  $x = \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$ 
D)  $x = - 20 , y = 3$ 
E)  $x = - \frac { 1 } { 20 } , y = \frac { 1 } { 3 }$

Question 16

Find the determinant of the matrix.   $\left[ \begin{array} { c c } 
- \frac { 7 } { 3 } & \frac { 14 } { 3 } \
- 1 & \frac { 1 } { 3 }
\end{array} \right]$

Accepted Answer

A)  $- \frac { 35 } { 17 }$ 
B)  $\frac { 13 } { 35 }$ 
C)  $\frac { 11 } { 35 }$ 
D)  $- \frac { 17 } { 35 }$ 
E)  $\frac { 35 } { 9 }$ 
A)  $- \frac { 35 } { 17 }$ 
B)  $\frac { 13 } { 35 }$ 
C)  $\frac { 11 } { 35 }$ 
D)  $- \frac { 17 } { 35 }$ 
E)  $\frac { 35 } { 9 }$

Question 17

Find the inverse of the matrix (if it exists).   $\left[ \begin{array} { c c } 
4 & - 1 \
- 3 & 1
\end{array} \right]$

Accepted Answer

A)   $\left[ \begin{array} { l l } 
1 & 1 \
3 & 4
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c } 
1 & 1 \
- 3 & 4
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c } 
- 1 & 1 \
3 & 4
\end{array} \right]$ 
D)   $\left[ \begin{array} { c c } 
1 & 1 \
3 & - 4
\end{array} \right]$ 
E) Does not exist 
A)   $\left[ \begin{array} { l l } 
1 & 1 \
3 & 4
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c } 
1 & 1 \
- 3 & 4
\end{array} \right]$ 
C)   $\left[ \begin{array} { c c } 
- 1 & 1 \
3 & 4
\end{array} \right]$ 
D)   $\left[ \begin{array} { c c } 
1 & 1 \
3 & - 4
\end{array} \right]$ 
E) Does not exist

Question 18

Find $| A |$ .   $A = \left[ \begin{array} { c c } 
- 4 & 0 \
0 & 6
\end{array} \right]$

Accepted Answer

A) -25 
B) -26 
C) -24 
D) -23 
E) -22 
A) -25 
B) -26 
C) -24 
D) -23 
E) -22

Question 19

Find the inverse of the matrix (if it exists).   $\left[ \begin{array} { c c c } 
- 5 & 0 & 0 \
2 & 0 & 0 \
1 & 5 & 7
\end{array} \right]$

Accepted Answer

A)   $\left[ \begin{array} { l l l } 
5 & 0 & 0 \
2 & 0 & 0 \
1 & 5 & 7
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
1 & 5 & 7
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
- 1 & - 5 & - 7
\end{array} \right]$ 
D)   $\left[ \begin{array} { l l l } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
- 1 & 5 & 7
\end{array} \right]$ 
E)  Does not exist 
A)   $\left[ \begin{array} { l l l } 
5 & 0 & 0 \
2 & 0 & 0 \
1 & 5 & 7
\end{array} \right]$ 
B)   $\left[ \begin{array} { c c c } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
1 & 5 & 7
\end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
- 1 & - 5 & - 7
\end{array} \right]$ 
D)   $\left[ \begin{array} { l l l } 
- 5 & 0 & 0 \
- 2 & 0 & 0 \
- 1 & 5 & 7
\end{array} \right]$ 
E)  Does not exist

Question 20

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

Accepted Answer

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

Write the augmented matrix for the system of linear equations. $\left\{ \begin{aligned}x - 3 y - 2 z & = - 2 \\4 y + 4 z & = 4 \\x + 4 z & = - 2\end{aligned} \right.$

Find 3A - 2B. $A = \left[ \begin{array} { c c } 6 & - 4 \\4 & 4 \\- 4 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 4 \\- 1 & - 6 \\2 & 10\end{array} \right]$

Fill in the blank(s) using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { c c c } 6 & 9 & 4 \\5 & - 4 & 7\end{array} \right]$ $\left[ \begin{array} { c c c } 2 & \cdots & \frac { 4 } { 3 } \\5 & - 4 & 7\end{array} \right]$

Use the matrix capabilities of a graphing utility to evaluate the expression.Round your results to three decimal places, if necessary. $55 \left( \left[ \begin{array} { c c } 12 & - 18 \\- 17 & 19\end{array} \right] + \left[ \begin{array} { c c } - 21 & 13 \\15 & 14\end{array} \right] \right)$

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { l } x + 2 y = 6 \\2 x + y = 9\end{array} \right.$

Evaluate the expression. $- 3 \left( \left[ \begin{array} { c c } - 6 & 0 \\4 & - 6\end{array} \right] + \left[ \begin{array} { c c } 7 & 3 \\- 5 & - 1\end{array} \right] \right) - 2 \left[ \begin{array} { c c } - 11 & - 10 \\14 & 5\end{array} \right]$

Find the determinant of the matrix. $\left[ \begin{array} { c c } - 5 & 2 \\\frac { 1 } { 2 } & 1\end{array} \right]$

Use the matrix capabilities of a graphing utility to find AB, if possible. $A = \left[ \begin{array} { c c c } - 7 & - 2 & - 8 \\2 & - 9 & 3 \\- 7 & - 8 & 6\end{array} \right] , B = \left[ \begin{array} { c c c } 4 & 4 & 1 \\- 9 & - 5 & 3 \\3 & - 2 & - 5\end{array} \right]$

Use a determinant to determine whether the points $( 1,4 ) , ( - 2,2 )$ and $( 7,8 )$ are collinear.Show all work.

Fill in the blank(s) using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { c c c } 1 & 1 & 1 \\5 & - 2 & 4\end{array} \right]$ $\left[ \begin{array} { c c c } 1 & 1 & 1 \\0 & \cdots & - 1\end{array} \right]$

Use a determinant and the given vertices of a triangle to find the area of the triangle.

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix $\left[ \begin{array} { c c c } 0 & 1 & 1 \\- 2 & 1 & 2 \\2 & - 1 & 0\end{array} \right]$ .Show all your work.

Find x and y. $\left[ \begin{array} { c c } x & - 2 \\7 & y\end{array} \right] = \left[ \begin{array} { c c } - 20 & - 2 \\7 & 3\end{array} \right]$

Find the determinant of the matrix. $\left[ \begin{array} { c c } - \frac { 7 } { 3 } & \frac { 14 } { 3 } \\- 1 & \frac { 1 } { 3 }\end{array} \right]$

Find the inverse of the matrix (if it exists). $\left[ \begin{array} { c c } 4 & - 1 \\- 3 & 1\end{array} \right]$

Find $| A |$ . $A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]$

Find the inverse of the matrix (if it exists). $\left[ \begin{array} { c c c } - 5 & 0 & 0 \\2 & 0 & 0 \\1 & 5 & 7\end{array} \right]$

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

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 8: Matrices and Determinants

Write the augmented matrix for the system of linear equations. {x−3y−2z=−24y+4z=4x+4z=−2\left\{ \begin{aligned}x - 3 y - 2 z & = - 2 \\4 y + 4 z & = 4 \\x + 4 z & = - 2\end{aligned} \right.⎩⎨⎧​x−3y−2z4y+4zx+4z​=−2=4=−2​

Find 3A - 2B. A=[6−444−44],B=[34−1−6210]A = \left[ \begin{array} { c c } 6 & - 4 \\4 & 4 \\- 4 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 4 \\- 1 & - 6 \\2 & 10\end{array} \right]A=​64−4​−444​​,B=​3−12​4−610​​

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. {x+2y=62x+y=9\left\{ \begin{array} { l } x + 2 y = 6 \\2 x + y = 9\end{array} \right.{x+2y=62x+y=9​

Find the determinant of the matrix. [−52121]\left[ \begin{array} { c c } - 5 & 2 \\\frac { 1 } { 2 } & 1\end{array} \right][−521​​21​]

Use a determinant to determine whether the points (1,4),(−2,2)( 1,4 ) , ( - 2,2 )(1,4),(−2,2) and (7,8)( 7,8 )(7,8) are collinear.Show all work. ​

Use a determinant and the given vertices of a triangle to find the area of the triangle.

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix [011−2122−10]\left[ \begin{array} { c c c } 0 & 1 & 1 \\- 2 & 1 & 2 \\2 & - 1 & 0\end{array} \right]​0−22​11−1​120​​ .Show all your work.

Find x and y. [x−27y]=[−20−273]\left[ \begin{array} { c c } x & - 2 \\7 & y\end{array} \right] = \left[ \begin{array} { c c } - 20 & - 2 \\7 & 3\end{array} \right][x7​−2y​]=[−207​−23​]

Find the determinant of the matrix. [−73143−113]\left[ \begin{array} { c c } - \frac { 7 } { 3 } & \frac { 14 } { 3 } \\- 1 & \frac { 1 } { 3 }\end{array} \right][−37​−1​314​31​​]

Find the inverse of the matrix (if it exists). [4−1−31]\left[ \begin{array} { c c } 4 & - 1 \\- 3 & 1\end{array} \right][4−3​−11​]

Find ∣A∣| A |∣A∣ . A=[−4006]A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]A=[−40​06​]

Find the inverse of the matrix (if it exists). [−500200157]\left[ \begin{array} { c c c } - 5 & 0 & 0 \\2 & 0 & 0 \\1 & 5 & 7\end{array} \right]​−521​005​007​​

Use Gauss-Jordan elimination on the augmented matrix [A|B] to solve for the matrix X. {−x1+x2=7−2x1+x2=0\left\{ \begin{aligned}- x _ { 1 } + x _ { 2 } & = 7 \\- 2 x _ { 1 } + x _ { 2 } & = 0\end{aligned} \right.{−x1​+x2​−2x1​+x2​​=7=0​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Write the augmented matrix for the system of linear equations. $\left\{ \begin{aligned}x - 3 y - 2 z & = - 2 \\4 y + 4 z & = 4 \\x + 4 z & = - 2\end{aligned} \right.$

Find 3A - 2B. $A = \left[ \begin{array} { c c } 6 & - 4 \\4 & 4 \\- 4 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 4 \\- 1 & - 6 \\2 & 10\end{array} \right]$

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{array} { l } x + 2 y = 6 \\2 x + y = 9\end{array} \right.$

Find the determinant of the matrix. $\left[ \begin{array} { c c } - 5 & 2 \\\frac { 1 } { 2 } & 1\end{array} \right]$

Use a determinant to determine whether the points $( 1,4 ) , ( - 2,2 )$ and $( 7,8 )$ are collinear.Show all work.

Find the uncoded 1 × 3 row matrices for the message "MERRY CHRISTMAS"; then encode the message using the encoding matrix $\left[ \begin{array} { c c c } 0 & 1 & 1 \\- 2 & 1 & 2 \\2 & - 1 & 0\end{array} \right]$ .Show all your work.

Find x and y. $\left[ \begin{array} { c c } x & - 2 \\7 & y\end{array} \right] = \left[ \begin{array} { c c } - 20 & - 2 \\7 & 3\end{array} \right]$

Find the determinant of the matrix. $\left[ \begin{array} { c c } - \frac { 7 } { 3 } & \frac { 14 } { 3 } \\- 1 & \frac { 1 } { 3 }\end{array} \right]$

Find the inverse of the matrix (if it exists). $\left[ \begin{array} { c c } 4 & - 1 \\- 3 & 1\end{array} \right]$

Find $| A |$ . $A = \left[ \begin{array} { c c } - 4 & 0 \\0 & 6\end{array} \right]$

Find the inverse of the matrix (if it exists). $\left[ \begin{array} { c c c } - 5 & 0 & 0 \\2 & 0 & 0 \\1 & 5 & 7\end{array} \right]$

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