Answer to Question #350097 in Linear Algebra for Youm

Question

Instructions

Upload photos of your answer sheet showing your name and solution. (2 items x 10 points)

1. Find A-B using the following matrices:

5

6 1

2

9

3

A=-3

5

8

B=|

81

4

3

3

4

67

-5

-1

2. Find AB using the following matrices:

A=

1 2

3

B=

+ Prepare answer

7

9

8

10

4 5 6

11

12

Answer 1

1.

$$A-B=\begin{pmatrix} 5 & 6 & 1 \\ -3 & 5 & 8 \\ 4 & 6 & 7 \\ \end{pmatrix}-\begin{pmatrix} 2 & 9 &3 \\ 4 & 0 & 3 \\ -5 & -1 & 3 \\ \end{pmatrix}$$

$$=\begin{pmatrix} 5-2 & 6-9 & 1-3 \\ -3-4 & 5-0 & 8-3 \\ 4-(-5) & 6-(-1) & 7-3 \\ \end{pmatrix}$$

$$=\begin{pmatrix} 3 & -3 & -2 \\ -7 & 5 & 5 \\ 9 & 7 & 4 \\ \end{pmatrix}$$

2.

$$AB=\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{pmatrix}\begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \\ \end{pmatrix}$$

$$=\begin{pmatrix} 1(7)+2(9)+3(11) & 1(8)+2(10)+3(12) \\ 4(7)+5(9)+6(11) & 4(8)+5(10)+6(12) \\ \end{pmatrix}$$

$$=\begin{pmatrix} 58 & 64 \\ 139 & 154 \end{pmatrix}$$