Question 1

Find the inverse of the invertible matrix.
-$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 4 & 1 & 0 \ 0 & 3 & 1 \end{array} \right]$

Accepted Answer

A)  $\left[ \begin{array} { r r r } 1 & 3 & - 12 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 4 & 1 & 0 \ 12 & - 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 4 & 1 & 0 \ 0 & 0 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 3 & - 1 & 0 \ - 12 & 4 & 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 1 & 3 & - 12 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 4 & 1 & 0 \ 12 & - 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 4 & 1 & 0 \ 0 & 0 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 3 & - 1 & 0 \ - 12 & 4 & 1 \end{array} \right]$

Question 2

Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { l l } 
2 & - 1 \
0 & - 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 6 } \ 0 & - \frac { 1 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & - \frac { 1 } { 3 } \ \frac { 1 } { 2 } & - \frac { 1 } { 6 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - \frac { 1 } { 3 } & - \frac { 1 } { 6 } \ 0 & \frac { 1 } { 2 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } \frac { 1 } { 2 } & - \frac { 1 } { 6 } \ 0 & - \frac { 1 } { 3 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 1 } { 2 } & \frac { 1 } { 6 } \ 0 & - \frac { 1 } { 3 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 0 & - \frac { 1 } { 3 } \ \frac { 1 } { 2 } & - \frac { 1 } { 6 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - \frac { 1 } { 3 } & - \frac { 1 } { 6 } \ 0 & \frac { 1 } { 2 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } \frac { 1 } { 2 } & - \frac { 1 } { 6 } \ 0 & - \frac { 1 } { 3 } \end{array} \right]$

Question 3

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these.
-$$A = \left[ \begin{array} { r } 
- 6.5 \
- 1.6 \
1.3
\end{array} \right]$$

Accepted Answer

A) 3; row matrix 
B) 1; row matrix 
C) 1 × 3; column matrix 
D) 3 × 1; column matrix 
A) 3; row matrix 
B) 1; row matrix 
C) 1 × 3; column matrix 
D) 3 × 1; column matrix

Question 4

Solve the problem.
-State University has a College of Arts & Sciences, a College of Business, and a College of Engineering. The percentage of students in each category are given by the following matrix.   The student population is distributed by class and age as given in the following matrix. $$\left. \begin{array} { l c c } 
& \text { Female } & \text { Male } \
\text { Freshman } & 420 & 780 \
\text { Sophomore } & 550 & 750 \
\text { Junior } & 850 & 620 \
\text { Senior } & 630 & 480
\end{array} \right]$$ How many female students are in the College of Business? How many male students are in the College of Arts & Sciences?

Accepted Answer

A) 1308 students; 622 students 
B) 690 students; 513 students 
C) 520 students; 690 students 
D) 622 students; 1427 students 
A) 1308 students; 622 students 
B) 690 students; 513 students 
C) 520 students; 690 students 
D) 622 students; 1427 students

Question 5

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

Accepted Answer

A)  $\left[ \begin{array} { l l } - 1 & 3 \ - 6 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 3 & - 1 \ 2 & - 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 2 & 0 \ - 2 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 2 & - 6 \ - 1 & - 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } - 1 & 3 \ - 6 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 3 & - 1 \ 2 & - 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 2 & 0 \ - 2 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 2 & - 6 \ - 1 & - 1 \end{array} \right]$

Question 6

Find the indicated matrix.
-Let $\mathrm { A } = \left[ \begin{array} { r r } - 1 & 3 \ 3 & 4 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l l } 0 & - 2 & 5 \ 1 & - 3 & 2 \end{array} \right]$. Find $\mathrm { AB }$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 3 & 4 \ - 7 & - 18 \ 1 & 23 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 0 & - 6 & 15 \ 3 & - 12 & 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 3 & - 7 & 1 \ 4 & - 18 & 23 \end{array} \right]$ 
D)  not defined 
A)  $\left[ \begin{array} { r r } 3 & 4 \ - 7 & - 18 \ 1 & 23 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 0 & - 6 & 15 \ 3 & - 12 & 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 3 & - 7 & 1 \ 4 & - 18 & 23 \end{array} \right]$ 
D)  not defined

Question 7

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

Accepted Answer

A)  $[ - 2 ]$ 
B)  $\left[ \begin{array} { r r } 0 & 3 \ 0 & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 3 \ 6 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 0 & 1 \end{array} \right]$ 
A)  $[ - 2 ]$ 
B)  $\left[ \begin{array} { r r } 0 & 3 \ 0 & - 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 3 \ 6 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & - 3 \ 0 & 1 \end{array} \right]$

Question 8

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.
-(1 × 1)(2 × 1)

Accepted Answer

A) 2 × 2 
B) not defined 
C) 1 × 2 
D) 2 × 1 
A) 2 × 2 
B) not defined 
C) 1 × 2 
D) 2 × 1

Question 9

Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { r r r } 
2 & - 1 & 0 \
- 1 & 1 & - 2 \
1 & 0 & - 1
\end{array} \right]$$

Accepted Answer

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

Question 10

Find the indicated matrix.
-Let $A = \left[ \begin{array} { r r } 0 & - 1 \ 5 & 0 \ 2 & 4 \end{array} \right] , B = \left[ \begin{array} { r r } - 4 & 0 \ 1 & 1 \ 5 & 5 \end{array} \right]$, and $C = \left[ \begin{array} { r r r } - 2 & 1 & 5 \ 0 & - 5 & - 1 \end{array} \right]$. Find $C ( A - B )$

Accepted Answer

A)  $\left[ \begin{array} { r r } - 19 & - 4 \ - 17 & 6 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - 13 & - 4 \ - 2 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & - 3 \ - 13 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 28 & 8 \ 16 & 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } - 19 & - 4 \ - 17 & 6 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } - 13 & - 4 \ - 2 & - 3 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & - 3 \ - 13 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 28 & 8 \ 16 & 1 \end{array} \right]$

Question 11

Find the indicated matrix.
-Let $A = \left[ \begin{array} { r r } 2 & - 8 \ 1 & 6 \ 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 3 & 2 \ 1 & - 1 \ 6 & 1 \end{array} \right]$. Find $A B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 9 & - 1 & 4 \ - 24 & - 5 & 1 \ 2 & 10 & 12 \end{array} \right]$ 
B)  not defined 
C)  $\left[ \begin{array} { r r r } - 24 & 10 & 4 \ 9 & - 5 & 12 \ 2 & - 1 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 4 & 10 & - 24 \ 12 & - 5 & 9 \ 1 & - 1 & 2 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 9 & - 1 & 4 \ - 24 & - 5 & 1 \ 2 & 10 & 12 \end{array} \right]$ 
B)  not defined 
C)  $\left[ \begin{array} { r r r } - 24 & 10 & 4 \ 9 & - 5 & 12 \ 2 & - 1 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 4 & 10 & - 24 \ 12 & - 5 & 9 \ 1 & - 1 & 2 \end{array} \right]$

Question 12

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

Accepted Answer

A)  $\left[ \begin{array} { r r r } 9 & 12 & 6 \ 7 & - 8 & - 5 \ - 1 & 14 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 7 & 0 & 6 \ 7 & - 8 & 1 \ 1 & 14 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 7 & 0 & 6 \ 9 & - 8 & - 5 \ - 1 & 14 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 9 & 12 & 6 \ 9 & - 8 & 1 \ 1 & 14 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 9 & 12 & 6 \ 7 & - 8 & - 5 \ - 1 & 14 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 7 & 0 & 6 \ 7 & - 8 & 1 \ 1 & 14 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 7 & 0 & 6 \ 9 & - 8 & - 5 \ - 1 & 14 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 9 & 12 & 6 \ 9 & - 8 & 1 \ 1 & 14 & 0 \end{array} \right]$

Question 13

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

Accepted Answer

A)  $\left[ \begin{array} { l l } - 1 & 12 \ - 9 & 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 5 & 2 \ - 5 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 13 & - 4 \ - 3 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 7 & - 14 \ 1 & - 14 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l } - 1 & 12 \ - 9 & 10 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 5 & 2 \ - 5 & 0 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 13 & - 4 \ - 3 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 7 & - 14 \ 1 & - 14 \end{array} \right]$

Question 14

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these.
-$$A = \left[ \begin{array} { r r r r r } 
9 & - 14 & 11 & - 6 & - 11 \
- 10 & 0 & 12 & - 3 & \pi \
- 13 & - 4 & 12 & 9 & - 6 \
\sqrt { 3 } & - 14 & - 3 & 11 & 15
\end{array} \right]$$

Accepted Answer

A) 4 × 5; none of these 
B) 5 × 4; none of these 
C) 4 × 4; square matrix 
D) 20; row matrix 
A) 4 × 5; none of these 
B) 5 × 4; none of these 
C) 4 × 4; square matrix 
D) 20; row matrix

Question 15

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

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 48 & 5 & 30 \ 12 & 48 & 30 \ 27 & 18 & - 25 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 73 & 19 & - 19 \ 3 & 36 & - 79 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 6 & - 5 & 5 \ - 3 & - 6 & 5 \ - 8 & - 6 & 5 \ - 4 & - 8 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 73 & 3 \ 19 & 36 \ - 19 & - 79 \end{array} \right]$ -9 -9 -5 
A)  $\left[ \begin{array} { r r r } - 48 & 5 & 30 \ 12 & 48 & 30 \ 27 & 18 & - 25 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 73 & 19 & - 19 \ 3 & 36 & - 79 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 6 & - 5 & 5 \ - 3 & - 6 & 5 \ - 8 & - 6 & 5 \ - 4 & - 8 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } - 73 & 3 \ 19 & 36 \ - 19 & - 79 \end{array} \right]$ -9 -9 -5

Question 16

Find the indicated matrix.
-Let $\mathrm { A } = \left[ \begin{array} { r r } - 4 & 1 \ 2 & 5 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } 6 & 2 \ 1 & 2 \end{array} \right]$. Find $\mathrm { A } + \mathrm { B }$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 2 & - 2 \ - 3 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 3 & 4 \ 3 & 7 \end{array} \right]$ 
C)  $[ 15 ]$ 
D)  $\left[ \begin{array} { l l } 2 & 3 \ 3 & 7 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 2 & - 2 \ - 3 & - 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 3 & 4 \ 3 & 7 \end{array} \right]$ 
C)  $[ 15 ]$ 
D)  $\left[ \begin{array} { l l } 2 & 3 \ 3 & 7 \end{array} \right]$

Question 17

Determine whether matrix B is the inverse of matrix A by finding the product AB.
-$A = \left[ \begin{array} { l l } - 5 & 1 \ - 7 & 1 \end{array} \right] , B = \left[ \begin{array} { l l } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \ \frac { 7 } { 2 } & - \frac { 5 } { 2 } \end{array} \right]$

Accepted Answer

A)  $B \neq A ^ { - 1 }$ 
B)  $B = A ^ { - 1 }$ 
A)  $B \neq A ^ { - 1 }$ 
B)  $B = A ^ { - 1 }$

Question 18

Matrix A is given. Find appropriate identity matrices IS1U1B1mS1U1B0 and IS1U1B1nS1U1B0 such that IS1U1B1mS1U1B0A = A and AIS1U1B1nS1U1B0 = A.
-$$A = \left[ \begin{array} { l l } 
8 & 3 \
3 & 8
\end{array} \right]$$

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Calculate $| \mathbf { A } |$
-$$A = \left| \begin{array} { l l l } 
8 & 0 & 0 \
5 & 8 & 7 \
9 & 4 & 6
\end{array} \right|$$

Accepted Answer

A) 608 
B) 165 
C) 160 
D) -160 
A) 608 
B) 165 
C) 160 
D) -160

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 0 \\ 4 & 1 & 0 \\ 0 & 3 & 1 \end{array} \right]$

Find the inverse of the invertible matrix. - $\left[ \begin{array} { l l } 2 & - 1 \\0 & - 3\end{array} \right]$

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r } - 6.5 \\- 1.6 \\1.3\end{array} \right]$

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

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 1 & 3 \\ 3 & 4 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l l } 0 & - 2 & 5 \\ 1 & - 3 & 2 \end{array} \right]$ . Find $\mathrm { AB }$ .

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

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. -(1 × 1)(2 × 1)

Find the inverse of the invertible matrix. - $\left[ \begin{array} { r r r } 2 & - 1 & 0 \\- 1 & 1 & - 2 \\1 & 0 & - 1\end{array} \right]$

Find the indicated matrix. -Let $A = \left[ \begin{array} { r r } 2 & - 8 \\ 1 & 6 \\ 0 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 3 & 2 \\ 1 & - 1 \\ 6 & 1 \end{array} \right]$ . Find $A B$ .

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

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - $A = \left[ \begin{array} { r r r r r } 9 & - 14 & 11 & - 6 & - 11 \\- 10 & 0 & 12 & - 3 & \pi \\- 13 & - 4 & 12 & 9 & - 6 \\\sqrt { 3 } & - 14 & - 3 & 11 & 15\end{array} \right]$

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

Find the indicated matrix. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 4 & 1 \\ 2 & 5 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } 6 & 2 \\ 1 & 2 \end{array} \right]$ . Find $\mathrm { A } + \mathrm { B }$ .

Determine whether matrix B is the inverse of matrix A by finding the product AB. - $A = \left[ \begin{array} { l l } - 5 & 1 \\ - 7 & 1 \end{array} \right] , B = \left[ \begin{array} { l l } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \\ \frac { 7 } { 2 } & - \frac { 5 } { 2 } \end{array} \right]$

Matrix A is given. Find appropriate identity matrices I_m and I_n such that I_mA = A and AI_n = A. - $A = \left[ \begin{array} { l l } 8 & 3 \\3 & 8\end{array} \right]$

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

Calculate $| \mathbf { A } |$ - $A = \left| \begin{array} { l l l } 8 & 0 & 0 \\5 & 8 & 7 \\9 & 4 & 6\end{array} \right|$

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Exam 8: Matrices

Find the inverse of the invertible matrix. - [100410031]\left[ \begin{array} { l l l } 1 & 0 & 0 \\ 4 & 1 & 0 \\ 0 & 3 & 1 \end{array} \right]​140​013​001​​

Find the inverse of the invertible matrix. - [2−10−3]\left[ \begin{array} { l l } 2 & - 1 \\0 & - 3\end{array} \right][20​−1−3​]

Determine the size of matrix A and tell whether it is a square matrix, row matrix, column matrix, or none of these. - A=[−6.5−1.61.3]A = \left[ \begin{array} { r } - 6.5 \\- 1.6 \\1.3\end{array} \right]A=​−6.5−1.61.3​​

Find the indicated matrix. -Let A=[−1322]A = \left[ \begin{array} { r r } - 1 & 3 \\ 2 & 2 \end{array} \right]A=[−12​32​] and B=[−20−11]B = \left[ \begin{array} { c c } - 2 & 0 \\ - 1 & 1 \end{array} \right]B=[−2−1​01​] . Find ABA BAB .

Find the indicated matrix. -Let A=[−1032]A = \left[ \begin{array} { r r } - 1 & 0 \\ 3 & 2 \end{array} \right]A=[−13​02​] and B=[−1331]B = \left[ \begin{array} { r r } - 1 & 3 \\ 3 & 1 \end{array} \right]B=[−13​31​] . Find A−BA - BA−B .