Question 1

Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { r r } 
1 & 4 \
1 & - 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 1 } { 9 } & \frac { 4 } { 9 } \ \frac { 1 } { 9 } & - \frac { 5 } { 9 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 5 } { 9 } & \frac { 4 } { 9 } \ \frac { 1 } { 9 } & - \frac { 1 } { 9 } \end{array} \right]$ 
C) $\left[ \begin{array} { r r } - \frac { 5 } { 9 } & - \frac { 4 } { 9 } \ - \frac { 1 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 5 } { 9 } & - \frac { 4 } { 9 } \ \frac { 1 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 1 } { 9 } & \frac { 4 } { 9 } \ \frac { 1 } { 9 } & - \frac { 5 } { 9 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 5 } { 9 } & \frac { 4 } { 9 } \ \frac { 1 } { 9 } & - \frac { 1 } { 9 } \end{array} \right]$ 
C) $\left[ \begin{array} { r r } - \frac { 5 } { 9 } & - \frac { 4 } { 9 } \ - \frac { 1 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 5 } { 9 } & - \frac { 4 } { 9 } \ \frac { 1 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ B

Question 2

Let (m × n) denote a matrix of size m × n. Find the size of the following product, or state that the product is not defined.
-(2 × 3)(3 × 2)

Accepted Answer

A) not defined 
B) 2 × 3 
C) 3 × 3 
D) 2 × 2 
A) not defined 
B) 2 × 3 
C) 3 × 3 
D) 2 × 2 D

Question 3

Find the indicated matrix.
-Let $A = \left[ \begin{array} { r r r } 1 & 3 & - 2 \ 3 & 0 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 3 & 0 \ - 2 & 1 \ 0 & 5 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r } - 7 & - 3 \ 25 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 25 \end{array} \right]$ 
C)  not defined 
D)  $\left[ \begin{array} { r r } - 3 & - 7 \ 9 & 25 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 7 & - 3 \ 25 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 3 & - 6 & 0 \ 0 & 0 & 25 \end{array} \right]$ 
C)  not defined 
D)  $\left[ \begin{array} { r r } - 3 & - 7 \ 9 & 25 \end{array} \right]$ D

Question 4

Calculate $| \mathbf { A } |$
-$$\mathrm { A } = \left| \begin{array} { l l l } 
2 & 2 & 2 \
6 & 6 & 1 \
3 & 2 & 1
\end{array} \right|$$

Accepted Answer

A) 10 
B) -10 
C) -22 
D) 94 
A) 10 
B) -10 
C) -22 
D) 94

Question 5

Solve the linear system using an inverse matrix.
-$$\begin{aligned}
x + 3 y & = - 8 \
4 x + 4 y & = 2
\end{aligned}$$

Accepted Answer

A)  $( 3 , - 1 )$ 
B)  $( - 3,1 )$ 
C)  $( 1 , - 3 )$ 
D)  $( - 1,3 )$ 
A)  $( 3 , - 1 )$ 
B)  $( - 3,1 )$ 
C)  $( 1 , - 3 )$ 
D)  $( - 1,3 )$

Question 6

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these.
-$$A = \left[ \begin{array} { r r } 
3 & 7 \
- 5 & - 3
\end{array} \right]$$

Accepted Answer

A) 1 × 2; none of these 
B) 2 × 2; square matrix 
C) 2; square matrix 
D) 4; square matrix 
A) 1 × 2; none of these 
B) 2 × 2; square matrix 
C) 2; square matrix 
D) 4; square matrix

Question 7

Find the inverse of the invertible matrix.
-$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 1 & 1 & 0 \ 1 & 1 & 1 \end{array} \right]$

Accepted Answer

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

Question 8

Find the indicated matrix.
-Let $A = \left[ \begin{array} { r r r } 3 & - 2 & 1 \ 0 & 4 & - 2 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 3 & 0 \ - 2 & 1 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 9 & - 6 \ - 6 & 8 \ 3 & - 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 9 & 0 \ 0 & 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & - 6 & 3 \ - 6 & 8 & - 4 \end{array} \right]$ 
D)  not defined 
A)  $\left[ \begin{array} { r r } 9 & - 6 \ - 6 & 8 \ 3 & - 4 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 9 & 0 \ 0 & 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & - 6 & 3 \ - 6 & 8 & - 4 \end{array} \right]$ 
D)  not defined

Question 9

Matrix A is given. Find appropriate identity matrices IS1U1B1mS1U1B0 and IS1U1B1nS1U1B0 such that IS1U1B1mS1U1B0A = A and AIS1U1B1nS1U1B0 = A.
-$$A = \left[ \begin{array} { l l l } 
- 7 & 5 & 1 \
- 4 & 4 & 1
\end{array} \right]$$

Accepted Answer

A)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$ 
B)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$ 
C)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$ 
D)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$ 
A)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$ 
B)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$ 
C)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$ 
D)  $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$

Question 10

Calculate $| \mathbf { A } |$
-$$\begin{array} { l } 
3 \mathrm { x } + 3 \mathrm { z } = 42 \
5 \mathrm { x } + 6 \mathrm { y } + 4 \mathrm { z } = 70 \
9 \mathrm { x } - 2 \mathrm { y } \quad = 70
\end{array}$$

Accepted Answer

A)  $( 9 , - 1,6 )$ 
B)  $( 8 , - 1 , - 6 )$ 
C)  $( 1,6,1 )$ 
D)  $( 8,1,6 )$ 
A)  $( 9 , - 1,6 )$ 
B)  $( 8 , - 1 , - 6 )$ 
C)  $( 1,6,1 )$ 
D)  $( 8,1,6 )$

Question 11

Find the indicated matrix.
-Let $A = \left[ \begin{array} { c c c } - 9 & 5 & - 6 \ - 7 & 7 & - 1 \ - 6 & 6 & - 6 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 4 & 3 & - 4 \ 4 & 8 & 5 \ 3 & 6 & 4 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 34 & - 23 & 37 \ - 3 & 29 & 59 \ - 18 & - 6 & 30 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 34 & - 3 & - 18 \ - 23 & - 3 & - 6 \ 37 & 59 & 30 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 36 & 15 & 24 \ - 28 & 56 & - 5 \ - 18 & 36 & - 24 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 9 & 5 & - 6 \ - 7 & 7 & - 1 \ - 6 & 6 & - 6 \ 4 & 3 & - 4 \ 4 & 8 & 5 \ 3 & 6 & 4 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 34 & - 23 & 37 \ - 3 & 29 & 59 \ - 18 & - 6 & 30 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 34 & - 3 & - 18 \ - 23 & - 3 & - 6 \ 37 & 59 & 30 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 36 & 15 & 24 \ - 28 & 56 & - 5 \ - 18 & 36 & - 24 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 9 & 5 & - 6 \ - 7 & 7 & - 1 \ - 6 & 6 & - 6 \ 4 & 3 & - 4 \ 4 & 8 & 5 \ 3 & 6 & 4 \end{array} \right]$

Question 12

Find the indicated matrix.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 0 & - 3 & 1 \ 5 & - 1 & 0 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r } 1 & 2 \ 0 & 1 \ 1 & - 1 \end{array} \right]$. Find $\mathrm { AB }$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 1 & 5 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & 10 \ 0 & - 1 \ 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 10 & - 5 & 1 \ 5 & - 1 & 0 \ - 5 & - 2 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 1 & - 4 \ 5 & 9 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 1 & 5 \ - 4 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 0 & 10 \ 0 & - 1 \ 0 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 10 & - 5 & 1 \ 5 & - 1 & 0 \ - 5 & - 2 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 1 & - 4 \ 5 & 9 \end{array} \right]$

Question 13

Find the indicated matrix.
-Let $\mathrm { A } = \left[ \begin{array} { r r } 3 & - 4 \ - 2 & 5 \end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r r } 5 & - 2 & 8 \ 1 & 0 & - 3 \end{array} \right]$, and $\mathrm { C } = \left[ \begin{array} { r r r } 7 & - 9 & 0 \ 3 & - 5 & 1 \ - 1 & 6 & 2 \end{array} \right]$. Find $\mathrm { AB } + \mathrm { BC }$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$

Question 14

Find the indicated matrix.
-Let $A = \left[ \begin{array} { r r r } 6 & 4 & 1 \ 12 & 2 & - 1 \ - 4 & 2 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 10 & - 4 & 1 \ - 4 & 0 & 2 \ 3 & 3 & - 2 \end{array} \right]$. Find $A - B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 4 & - 8 & 0 \ 16 & 2 & - 3 \ - 7 & 1 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 4 & 0 & 0 \ 16 & 2 & - 3 \ 1 & - 1 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 16 & 0 & 2 \ 8 & 2 & 1 \ - 1 & 5 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 4 & 8 & 0 \ 16 & 2 & - 3 \ - 7 & - 1 & 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 4 & - 8 & 0 \ 16 & 2 & - 3 \ - 7 & 1 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 4 & 0 & 0 \ 16 & 2 & - 3 \ 1 & - 1 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 16 & 0 & 2 \ 8 & 2 & 1 \ - 1 & 5 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 4 & 8 & 0 \ 16 & 2 & - 3 \ - 7 & - 1 & 5 \end{array} \right]$

Question 15

Solve the linear system using an inverse matrix.
-x + 2y + 3z = -1 
x + y + z = -3 
-x + y + 2z = 11

Accepted Answer

A) (30, -47, -16) 
B) (7, 4, 0) 
C) (-1, -12, -22) 
D) (-9, 10, -4) 
A) (30, -47, -16) 
B) (7, 4, 0) 
C) (-1, -12, -22) 
D) (-9, 10, -4)

Question 16

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these.
-$$A = \left[ \begin{array} { l l l l } 
3 & - 3 & 9 & 7
\end{array} \right]$$

Accepted Answer

A) 4 × 1; column matrix 
B) 1 × 4; row matrix 
C) 1; square matrix 
D) 4; row matrix 
A) 4 × 1; column matrix 
B) 1 × 4; row matrix 
C) 1; square matrix 
D) 4; row matrix

Question 17

Let (m × n) denote a matrix of size m × n. Find the size of the following product, or state that the product is not defined.
-(3 × 4)(3 × 4)

Accepted Answer

A) 3 × 4 
B) 3 × 3 
C) 4 × 3 
D) not defined 
A) 3 × 4 
B) 3 × 3 
C) 4 × 3 
D) not defined

Question 18

Use Cramer's rule to solve the linear system.
-$$2 x + 2 y = 32$$
$2 x - 3 y = - 13$

Accepted Answer

A)  $( - 7 , - 9 )$ 
B)  $( - 9,7 )$ 
C)  $( 9,7 )$ 
D)  $( 7,9 )$ 
A)  $( - 7 , - 9 )$ 
B)  $( - 9,7 )$ 
C)  $( 9,7 )$ 
D)  $( 7,9 )$

Question 19

Calculate $| \mathbf { A } |$
-$$\begin{array} { l } 
- 2 x - 9 y + 8 z = - 32 \
7 x + 3 y + 4 z = 101 \
4 x - 9 y - 2 z = - 28
\end{array}$$

Accepted Answer

A)  $( 9 , - 6 , - 5 )$ 
B)  $( 10,4,5 )$ 
C)  $( 9,6,5 )$ 
D)  $( 6,5,6 )$ 
A)  $( 9 , - 6 , - 5 )$ 
B)  $( 10,4,5 )$ 
C)  $( 9,6,5 )$ 
D)  $( 6,5,6 )$

Question 20

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these.
-$$A = \left[ \begin{array} { r r r } 
5 & 5 & - 3 \
- 4 & - 7 & 1
\end{array} \right]$$

Accepted Answer

A) 2 × 3; none of these 
B) 3 × 2; none of these 
C) 3; row matrix 
D) 6; row matrix 
A) 2 × 3; none of these 
B) 3 × 2; none of these 
C) 3; row matrix 
D) 6; row matrix

Find the inverse of the invertible matrix. - $\left[ \begin{array} { r r } 1 & 4 \\1 & - 5\end{array} \right]$

Let (m × n) denote a matrix of size m × n. Find the size of the following product, or state that the product is not defined. -(2 × 3)(3 × 2)

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r r } 1 & 3 & - 2 \\ 3 & 0 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 3 & 0 \\ - 2 & 1 \\ 0 & 5 \end{array} \right]$ . Find $A B$ .

Calculate $| \mathbf { A } |$ - $\mathrm { A } = \left| \begin{array} { l l l } 2 & 2 & 2 \\6 & 6 & 1 \\3 & 2 & 1\end{array} \right|$

Solve the linear system using an inverse matrix. - x+3y =-8 4x+4y =2

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r r } 3 & 7 \\- 5 & - 3\end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{array} \right]$

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r r } 3 & - 2 & 1 \\ 0 & 4 & - 2 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 3 & 0 \\ - 2 & 1 \end{array} \right]$ . Find $A B$ .

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { l l l } - 7 & 5 & 1 \\- 4 & 4 & 1\end{array} \right]$

Calculate $| \mathbf { A } |$ - 3+3=42 5+6+4=70 9-2=70

Find the indicated matrix. -Let $A = \left[ \begin{array} { c c c } - 9 & 5 & - 6 \\ - 7 & 7 & - 1 \\ - 6 & 6 & - 6 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 4 & 3 & - 4 \\ 4 & 8 & 5 \\ 3 & 6 & 4 \end{array} \right]$ . Find $A B$ .

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r r } 0 & - 3 & 1 \\ 5 & - 1 & 0 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r } 1 & 2 \\ 0 & 1 \\ 1 & - 1 \end{array} \right]$ . Find $\mathrm { AB }$ .

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r r } 6 & 4 & 1 \\ 12 & 2 & - 1 \\ - 4 & 2 & 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 10 & - 4 & 1 \\ - 4 & 0 & 2 \\ 3 & 3 & - 2 \end{array} \right]$ . Find $A - B$ .

Solve the linear system using an inverse matrix. -x + 2y + 3z = -1 x + y + z = -3 -x + y + 2z = 11

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { l l l l } 3 & - 3 & 9 & 7\end{array} \right]$

Let (m × n) denote a matrix of size m × n. Find the size of the following product, or state that the product is not defined. -(3 × 4)(3 × 4)

Use Cramer's rule to solve the linear system. - $2 x + 2 y = 32$ $2 x - 3 y = - 13$

Calculate $| \mathbf { A } |$ - -2x-9y+8z=-32 7x+3y+4z=101 4x-9y-2z=-28

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r r r } 5 & 5 & - 3 \\- 4 & - 7 & 1\end{array} \right]$

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Exam 8: Matrices

Find the inverse of the invertible matrix. - [141−5]\left[ \begin{array} { r r } 1 & 4 \\1 & - 5\end{array} \right][11​4−5​]