Question 1

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
w - 2 x - 3 y = - 5 \
- 4 x - 2 y = - 16 \
- 2 x + 4 y - 5 z = - 28 \
5 w - 2 x + 2 y - 5 z = - 13
\end{array}$$

Accepted Answer

A)  $\{ ( 3,4,0 , - 4 ) \}$ 
B)  $\{ ( 3,4,0,4 ) \}$ 
C)  $\{ ( - 3 , - 4,0 , - 4 ) \}$ 
D)  $\{ ( - 3 , - 4,0,4 ) \}$ 
A)  $\{ ( 3,4,0 , - 4 ) \}$ 
B)  $\{ ( 3,4,0,4 ) \}$ 
C)  $\{ ( - 3 , - 4,0 , - 4 ) \}$ 
D)  $\{ ( - 3 , - 4,0,4 ) \}$ B

Question 2

Solve the problem.
-Matrix G represents the gas mileage (in gal/mi) for city and highway driving for four models of car. Matrix $N _ { 1 }$ represents the number of city and highway miles driven for one trip. Matrix $N _ { 3 }$represents The number of city and highway miles driven for three trips. $\quad $$\text { City}$$\quad $ $\text {Highway }$
$G=\left[\begin{array}{cc} 
\frac{1}{23} & \frac{1}{30} \\
\frac{1}{24} & \frac{1}{37} \\
\frac{1}{24} & \frac{1}{30} \\
\frac{1}{25} & \frac{1}{31}
\end{array}\right] \text { Car } 1 \text { automatic } 1 \text { manual }$
 $N _ { 1 } = \left[ \begin{array} { l } 110 \ 260 \end{array} \right] \begin{array} { l } \text { Number of city miles } \ \text { Number of highway miles } \end{array}$

a. Find the product $G N _ { 1 }$ and interpret its meaning. Round each entry to 1 decimal place.
b. Find the product $G N _ { 3 }$ and interpret its meaning. Round each entry to 1 decimal place. This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips.

Accepted Answer

A)  a.
$ G N_{1}=\left[\begin{array}{l}13.4 \ 11.6 \ 13.3 \ 12.8\end{array}\right] $

This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway.
$$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
12.3 & 16.9 & 13.4 \
10.3 & 14.5 & 11.6 \
12.2 & 16.7 & 13.3 \
11.8 & 16.1 & 12.8
\end{array} \right] \text {. }$$ 
B)  a. $G N_{1}=\left[\begin{array}{l}
15.0 \
13.8 \
14.5 \
13.9
\end{array}\right]$
 This matrix represents the number of gallons of gasoline used for each model of car for 260 mi driven
In the city and 110 mi driven on the highway. b.
$G N _ { 3 } = \left[ \begin{array} { c c c } 13.4 & 16.9 & 12.3 \ 11.6 & 14.5 & 10.3 \ 13.3 & 16.7 & 12.2 \ 12.8 & 16.1 & 11.8 \end{array} \right]$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. 
C)  a. $G N_{1}=\left[\begin{array}{l}
13.4 \
11.6 \
13.3 \
12.8
\end{array}\right]$  This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway. $$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
16.9 & 13.4 & 12.3 \
14.5 & 11.6 & 10.3 \
16.7 & 13.3 & 12.2 \
16.1 & 12.8 & 11.8
\end{array} \right]$$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. 
D)  a.
$G N _ { 1 } = \left[ \begin{array} { l } 13.4 \ 11.6 \ 13.3 \ 12.8 \end{array} \right]$ This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway. $$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
13.4 & 16.9 & 12.3 \
11.6 & 14.5 & 10.3 \
13.3 & 16.7 & 12.2 \
12.8 & 16.1 & 11.8
\end{array} \right] \text {. }$$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. 
A)  a.
$ G N_{1}=\left[\begin{array}{l}13.4 \ 11.6 \ 13.3 \ 12.8\end{array}\right] $

This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway.
$$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
12.3 & 16.9 & 13.4 \
10.3 & 14.5 & 11.6 \
12.2 & 16.7 & 13.3 \
11.8 & 16.1 & 12.8
\end{array} \right] \text {. }$$ 
B)  a. $G N_{1}=\left[\begin{array}{l}
15.0 \
13.8 \
14.5 \
13.9
\end{array}\right]$
 This matrix represents the number of gallons of gasoline used for each model of car for 260 mi driven
In the city and 110 mi driven on the highway. b.
$G N _ { 3 } = \left[ \begin{array} { c c c } 13.4 & 16.9 & 12.3 \ 11.6 & 14.5 & 10.3 \ 13.3 & 16.7 & 12.2 \ 12.8 & 16.1 & 11.8 \end{array} \right]$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. 
C)  a. $G N_{1}=\left[\begin{array}{l}
13.4 \
11.6 \
13.3 \
12.8
\end{array}\right]$  This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway. $$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
16.9 & 13.4 & 12.3 \
14.5 & 11.6 & 10.3 \
16.7 & 13.3 & 12.2 \
16.1 & 12.8 & 11.8
\end{array} \right]$$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. 
D)  a.
$G N _ { 1 } = \left[ \begin{array} { l } 13.4 \ 11.6 \ 13.3 \ 12.8 \end{array} \right]$ This matrix represents the number of gallons of gasoline used for each model of car for 110 mi driven
In the city and 260 mi driven on the highway. $$\text { b. } G N _ { 3 } = \left[ \begin{array} { l l l } 
13.4 & 16.9 & 12.3 \
11.6 & 14.5 & 10.3 \
13.3 & 16.7 & 12.2 \
12.8 & 16.1 & 11.8
\end{array} \right] \text {. }$$ This matrix represents the number of gallons of gasoline used for each model of car for each of the three
Trips. D

Question 3

Choose the one alternative that best completes the statement or answers the question.
Evaluate the determinant of the given matrix.
-$$A = \left[ \begin{array} { r r } 
u & - 5 \
9 & u
\end{array} \right]$$

Accepted Answer

A)  $- u ^ { 2 } + 45$ 
B)  $u ^ { 2 } + 45$ 
C)  $u ^ { 2 } - 45$ 
D)  $- u ^ { 2 } - 45$ 
A)  $- u ^ { 2 } + 45$ 
B)  $u ^ { 2 } + 45$ 
C)  $u ^ { 2 } - 45$ 
D)  $- u ^ { 2 } - 45$ B

Question 4

Choose the one alternative that best completes the statement or answers the question.
Give the order of the matrix.
-$$\left[ \begin{array} { r r r } 
8 & 7 & 7 \
- 4 & 8 & - 6
\end{array} \right]$$

Accepted Answer

A)  6 
B)  5 
C)  $2 \times 3$ 
D)  $3 \times 2$ 
A)  6 
B)  5 
C)  $2 \times 3$ 
D)  $3 \times 2$

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Suppose that the matrix equation AX = B represents a system of n linear equations in n variables with a unique solution. Then X =________ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by
using another method.
-$\begin{array} { l } 
- 9 x + 27 y + 9 z = 7 \
18 x + 45 y = 14 \
27 x + 9 y - 18 z = - 7
\end{array}$

Accepted Answer

A) {  } 
B)  $\left\{ \left( - \frac { 7 } { 9 } , 0 , - \frac { 14 } { 9 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 7 } { 9 } , 0 , \frac { 14 } { 9 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 7 } { 9 } + z , 0 , z \mid z \right. \right.$ is any real number $\}$ 
A) {  } 
B)  $\left\{ \left( - \frac { 7 } { 9 } , 0 , - \frac { 14 } { 9 } \right) \right\}$ 
C)  $\left\{ \left( \frac { 7 } { 9 } , 0 , \frac { 14 } { 9 } \right) \right\}$ 
D)  $\left\{ \left( - \frac { 7 } { 9 } + z , 0 , z \mid z \right. \right.$ is any real number $\}$

Question 7

Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { l l } 
4 & 1 \
2 & 2
\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 
3 & - 2 \
- 11 & 8
\end{array} \right]$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 8

Solve the problem.
-  
a. Write a matrix A that represents the coordinates of the quadrilateral. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A.
b. What operation on A will shift the graph of the quadrilateral 2 units upward?

Accepted Answer

A)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$
b. $A + \left[ \begin{array} { l l l l } 2 & 2 & 2 & 2 \ 0 & 0 & 0 & 0 \end{array} \right]$ 
B)  a. $A = \left[ \begin{array} { r r r r } 2 & 5 & 3 & - 2 \ - 3 & 1 & 4 & - 2 \end{array} \right]$

b. $A + \left[ \begin{array} { l l l l } 2 & 2 & 2 & 2 \ 0 & 0 & 0 & 0 \end{array} \right]$ 
C)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$
b. $A + \left[ \begin{array} { r r r r } 0 & 0 & 0 & 0 \ - 2 & - 2 & - 2 & - 2 \end{array} \right]$ 
D)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$

b. $A + \left[ \begin{array} { l l l l } 0 & 0 & 0 & 0 \ 2 & 2 & 2 & 2 \end{array} \right]$ 
A)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$
b. $A + \left[ \begin{array} { l l l l } 2 & 2 & 2 & 2 \ 0 & 0 & 0 & 0 \end{array} \right]$ 
B)  a. $A = \left[ \begin{array} { r r r r } 2 & 5 & 3 & - 2 \ - 3 & 1 & 4 & - 2 \end{array} \right]$

b. $A + \left[ \begin{array} { l l l l } 2 & 2 & 2 & 2 \ 0 & 0 & 0 & 0 \end{array} \right]$ 
C)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$
b. $A + \left[ \begin{array} { r r r r } 0 & 0 & 0 & 0 \ - 2 & - 2 & - 2 & - 2 \end{array} \right]$ 
D)  a. $A = \left[ \begin{array} { r r r r } - 3 & 1 & 4 & - 2 \ 2 & 5 & 3 & - 2 \end{array} \right]$

b. $A + \left[ \begin{array} { l l l l } 0 & 0 & 0 & 0 \ 2 & 2 & 2 & 2 \end{array} \right]$

Question 9

Solve the problem.
-Andre borrowed $40,000 to buy a truck for his business. He borrowed from his parents who charge him 3% simple interest. He borrowed from a credit union that charges 4% simple interest, and he
Borrowed from a bank that charges 6% simple interest. He borrowed four times as much from his
Parents as from the bank, and the amount of interest he paid at the end of 1 yr was $1,560. How
Much did he borrow from each source?

Accepted Answer

A)  He borrowed $4,000 from his parents, $35,000 from the credit union, and $1,000 from the bank. 
B)  He borrowed 1,500 from his parents, 32,500 from the credit union, and 6,000 from the bank. 
C)  He borrowed 6,000 from his parents, 32,500 from the credit union, and 1,500 from the bank. 
D)  He borrowed $8,000 from his parents, $30,000 from the credit union, and $2,000 from the bank. 
A)  He borrowed $4,000 from his parents, $35,000 from the credit union, and $1,000 from the bank. 
B)  He borrowed 1,500 from his parents, 32,500 from the credit union, and 6,000 from the bank. 
C)  He borrowed 6,000 from his parents, 32,500 from the credit union, and 1,500 from the bank. 
D)  He borrowed $8,000 from his parents, $30,000 from the credit union, and $2,000 from the bank.

Question 10

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$$A = \left[ \begin{array} { l l } 
- 3 & 4 \
- 5 & 3
\end{array} \right]$$

Accepted Answer

A)  $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$ 
B)  $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & - \frac { 4 } { 11 } \ \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$ 
C)  Singular matrix 
D)  $A ^ { - 1 } = \left[ \begin{array} { c c } - \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & \frac { 3 } { 11 } \end{array} \right]$ 
A)  $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$ 
B)  $A ^ { - 1 } = \left[ \begin{array} { c c } \frac { 3 } { 11 } & - \frac { 4 } { 11 } \ \frac { 5 } { 11 } & - \frac { 3 } { 11 } \end{array} \right]$ 
C)  Singular matrix 
D)  $A ^ { - 1 } = \left[ \begin{array} { c c } - \frac { 3 } { 11 } & \frac { 4 } { 11 } \ - \frac { 5 } { 11 } & \frac { 3 } { 11 } \end{array} \right]$

Question 11

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $A = \left[ a _ { i j } \right]$, then the value $( - 1 ) ^ { i + j } M _ { i j }$ is called the ــــــــــــــــــ of the element $a _ { i j }$

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Solve the system using Gaussian elimination or Gauss-Jordan elimination.
-$\begin{array} { l } 
x _ { 1 } - 5 x _ { 2 } + 2 x _ { 3 } = 6 \
5 x _ { 2 } - 2 x _ { 3 } = - 1 \
- 3 x _ { 2 } - 4 x _ { 3 } - 5 x _ { 4 } = - 30 \
5 x _ { 1 } + 4 x _ { 2 } + 4 x _ { 3 } + 5 x _ { 4 } = 56
\end{array}$

Accepted Answer

A)  $\{ ( 5,1 , - 3 , - 3 ) \}$ 
B)  $\{ ( - 5 , - 1 , - 3 , - 3 ) \}$ 
C)  $\{ ( - 5 , - 1,3,3 ) \}$ 
D)  $\{ ( 5,1,3,3 ) \}$ 
A)  $\{ ( 5,1 , - 3 , - 3 ) \}$ 
B)  $\{ ( - 5 , - 1 , - 3 , - 3 ) \}$ 
C)  $\{ ( - 5 , - 1,3,3 ) \}$ 
D)  $\{ ( 5,1,3,3 ) \}$

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If a system of linear equations has infinitely many solutions, then the equations are said to be________

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Evaluate the determinant of the given matrix and state whether the matrix is invertible.
-$$A = \left[ \begin{array} { r r r r } 
7 & 0 & 2 & - 7 \
- 3 & - 4 & 9 & 5 \
0 & - 1 & 6 & 5 \
9 & 5 & 6 & 2
\end{array} \right]$$

Accepted Answer

A)  648 , No 
B)  $648 , \mathrm { Yes }$ 
C)  $1,026 , \mathrm { Yes }$ 
D)  $1,026 , \mathrm { No }$ 
A)  648 , No 
B)  $648 , \mathrm { Yes }$ 
C)  $1,026 , \mathrm { Yes }$ 
D)  $1,026 , \mathrm { No }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $A = \left[ a _ { i j } \right.$ , the ________of the element $a _ { i j }$ is the determinant obtained by deleting the $i^ \text { th }$ row and jth column.

Accepted Answer

Question 16

Find the additive inverse of A.
-$$A = \left[ \begin{array} { r r } 
9 & 2 \
- 4 & 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } - 9 & - 2 \ 4 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 9 & - 2 \ 4 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 2 \ 4 & 5 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 9 & 2 \ - 4 & - 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 9 & - 2 \ 4 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 9 & - 2 \ 4 & 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 9 & 2 \ 4 & 5 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 9 & 2 \ - 4 & - 5 \end{array} \right]$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-$$\text { For a } 2 \times 2 \text { matrix } A = \left[ \begin{array} { l l } 
a & b \
c & d
\end{array} \right] , | A | = \left| \begin{array} { l l } 
a & b \
c & d
\end{array} \right| =$$ــــــــــــــــــــــ

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Write a system of linear equations represented by the augmented matrix.
-$$\left[ \begin{array} { r r | r } 
- 7 & 9 & - 1 \
5 & - 6 & 7
\end{array} \right]$$

Accepted Answer

A)  $- 7 x - 9 y = 1$
$5 x + 6 y = 7$ 
B)  $- 7 x - 9 y = 1$
$5 x + 6 y = - 7$ 
C)  $- 7 x + 9 y = - 1$
$5 x - 6 y = - 7$ 
D)  $- 7 x + 9 y = - 1$
$5 x - 6 y = 7$ 
A)  $- 7 x - 9 y = 1$
$5 x + 6 y = 7$ 
B)  $- 7 x - 9 y = 1$
$5 x + 6 y = - 7$ 
C)  $- 7 x + 9 y = - 1$
$5 x - 6 y = - 7$ 
D)  $- 7 x + 9 y = - 1$
$5 x - 6 y = 7$

Question 19

Solve the system using Gaussian elimination or Gauss-Jordan elimination.
-$$\begin{array} { l } 
- 4 x - 6 y + 5 z = 13 \
8 x + 4 y - 7 z = - 7 \
4 x - 2 y - 2 z = - 15
\end{array}$$

Accepted Answer

A)  $\{ ( 8,4,5 ) \}$ 
B)  $\{ ( 8,5,4 ) \}$ 
C)  { } 
D)  $\{ ( 5,8,4 ) \}$ 
A)  $\{ ( 8,4,5 ) \}$ 
B)  $\{ ( 8,5,4 ) \}$ 
C)  { } 
D)  $\{ ( 5,8,4 ) \}$

Question 20

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
-$$A = \left[ \begin{array} { r r r } 
4 & - 1 & 5 \
1 & 1 & - 2 \
- 1 & 1 & 0
\end{array} \right]$$

Accepted Answer

A)  $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & - \frac { 5 } { 16 } \end{array} \right]$ 
B)  Singular matrix 
C)  $A ^ { - 1 } = \left[ \begin{array} { c c c } - \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ - \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ - \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$ 
D)  $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$ 
A)  $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & - \frac { 5 } { 16 } \end{array} \right]$ 
B)  Singular matrix 
C)  $A ^ { - 1 } = \left[ \begin{array} { c c c } - \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ - \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ - \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$ 
D)  $A ^ { - 1 } = \left[ \begin{array} { c c c } \frac { 1 } { 8 } & \frac { 5 } { 16 } & - \frac { 3 } { 16 } \ \frac { 1 } { 8 } & \frac { 5 } { 16 } & \frac { 13 } { 16 } \ \frac { 1 } { 8 } & - \frac { 3 } { 16 } & \frac { 5 } { 16 } \end{array} \right]$

Solve the system by using the inverse of the coefficient matrix. - w-2x-3y=-5 -4x-2y=-16 -2x+4y-5z=-28 5w-2x+2y-5z=-13

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { r r } u & - 5 \\9 & u\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Give the order of the matrix. - $\left[ \begin{array} { r r r } 8 & 7 & 7 \\- 4 & 8 & - 6\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that the matrix equation AX = B represents a system of n linear equations in n variables with a unique solution. Then X =________ .

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. - -9x+27y+9z=7 18x+45y=14 27x+9y-18z=-7

Determine whether A and B are inverses. - $A = \left[ \begin{array} { l l } 4 & 1 \\2 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 3 & - 2 \\- 11 & 8\end{array} \right]$

Solve the problem. - a. Write a matrix A that represents the coordinates of the quadrilateral. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A. b. What operation on A will shift the graph of the quadrilateral 2 units upward?

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $A = \left[ a _ { i j } \right]$ , then the value $( - 1 ) ^ { i + j } M _ { i j }$ is called the ــــــــــــــــــ of the element $a _ { i j }$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -5+2=6 5-2=-1 -3-4-5=-30 5+4+4+5=56

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If a system of linear equations has infinitely many solutions, then the equations are said to be________

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $A = \left[ a _ { i j } \right.$ , the ________of the element $a _ { i j }$ is the determinant obtained by deleting the $i^ \text { th }$ row and j^th column.

Find the additive inverse of A. - $A = \left[ \begin{array} { r r } 9 & 2 \\- 4 & 5\end{array} \right]$

Write a system of linear equations represented by the augmented matrix. - $\left[ \begin{array} { r r | r } - 7 & 9 & - 1 \\5 & - 6 & 7\end{array} \right]$

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -4x-6y+5z=13 8x+4y-7z=-7 4x-2y-2z=-15

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

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Exam 6: Matrices and Determinants and Applications

Solve the system by using the inverse of the coefficient matrix. - w-2x-3y=-5 -4x-2y=-16 -2x+4y-5z=-28 5w-2x+2y-5z=-13

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - A=[u−59u]A = \left[ \begin{array} { r r } u & - 5 \\9 & u\end{array} \right]A=[u9​−5u​]

Choose the one alternative that best completes the statement or answers the question. Give the order of the matrix. - [877−48−6]\left[ \begin{array} { r r r } 8 & 7 & 7 \\- 4 & 8 & - 6\end{array} \right][8−4​78​7−6​]

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that the matrix equation AX = B represents a system of n linear equations in n variables with a unique solution. Then X =________ .

Solve the system, if possible, by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. - -9x+27y+9z=7 18x+45y=14 27x+9y-18z=-7

Determine whether A and B are inverses. - A=[4122] and B=[3−2−118]A = \left[ \begin{array} { l l } 4 & 1 \\2 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 3 & - 2 \\- 11 & 8\end{array} \right]A=[42​12​] and B=[3−11​−28​]

Solve the problem. - a. Write a matrix A that represents the coordinates of the quadrilateral. Place the x-coordinate of each point in the first row of A and the corresponding y-coordinate in the second row of A. b. What operation on A will shift the graph of the quadrilateral 2 units upward?

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - A=[−34−53]A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]A=[−3−5​43​]

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -5+2=6 5-2=-1 -3-4-5=-30 5+4+4+5=56

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If a system of linear equations has infinitely many solutions, then the equations are said to be________

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - A=[702−7−3−4950−1659562]A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]A=​7−309​0−4−15​2966​−7552​​

Find the additive inverse of A. - A=[92−45]A = \left[ \begin{array} { r r } 9 & 2 \\- 4 & 5\end{array} \right]A=[9−4​25​]

Write a system of linear equations represented by the augmented matrix. - [−79−15−67]\left[ \begin{array} { r r | r } - 7 & 9 & - 1 \\5 & - 6 & 7\end{array} \right][−75​9−6​−17​]

Solve the system using Gaussian elimination or Gauss-Jordan elimination. - -4x-6y+5z=13 8x+4y-7z=-7 4x-2y-2z=-15

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - A=[4−1511−2−110]A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]A=​41−1​−111​5−20​​

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Evaluate the determinant of the given matrix. - $A = \left[ \begin{array} { r r } u & - 5 \\9 & u\end{array} \right]$

Choose the one alternative that best completes the statement or answers the question. Give the order of the matrix. - $\left[ \begin{array} { r r r } 8 & 7 & 7 \\- 4 & 8 & - 6\end{array} \right]$

Determine whether A and B are inverses. - $A = \left[ \begin{array} { l l } 4 & 1 \\2 & 2\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 3 & - 2 \\- 11 & 8\end{array} \right]$

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { l l } - 3 & 4 \\- 5 & 3\end{array} \right]$

Evaluate the determinant of the given matrix and state whether the matrix is invertible. - $A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]$

Find the additive inverse of A. - $A = \left[ \begin{array} { r r } 9 & 2 \\- 4 & 5\end{array} \right]$

Write a system of linear equations represented by the augmented matrix. - $\left[ \begin{array} { r r | r } - 7 & 9 & - 1 \\5 & - 6 & 7\end{array} \right]$

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular. - $A = \left[ \begin{array} { r r r } 4 & - 1 & 5 \\1 & 1 & - 2 \\- 1 & 1 & 0\end{array} \right]$