Answer to Question #275329 in Linear Algebra for Good heart

Question

Given that A= 3 ‐1 2 and B= 4 [‐1 2]

[5 1 7] 5 1 3

I. Evaluate 3A and 2B

ii. 3A‐2B

Given that C= 1 6

[3 9]

4 -3 Evaluate CB

Answer 1

$$A=\begin{bmatrix} 3 & -1 & 2\\ 5 & 1& 3 \end{bmatrix}, B=\begin{bmatrix} 4 & -1 & 2\\ 5 & 1 & 7 \end{bmatrix}$$

$$C=\begin{bmatrix} 1 & 6\\ 3 & 9 \\ 4 & -3 \end{bmatrix}$$

i.

$$3A=\begin{bmatrix} 9 & -3 & 6\\ 15 & 3 & 9 \end{bmatrix}$$

$$2B=\begin{bmatrix} 8 & -2 & 4\\ 10 & 2 & 14 \end{bmatrix}$$

ii.

$$3A-2B=\begin{bmatrix} 1 & -1 & 2\\ 5 & 1 & -5 \end{bmatrix}$$

iii.

$$CB=\begin{bmatrix} 1 & 6\\ 3 & 9 \\ 4 & -3 \end{bmatrix}\begin{bmatrix} 4 & -1 & 2\\ 5 & 1 & 7 \end{bmatrix}$$

$$=\begin{bmatrix} 1(4)+6(5) & 1(-1)+6(1) & 1(2)+6(7)\\ 3(4)+9(5) & 3(-1)+9(1) & 3(2)+9(7) \\ 4(4)-3(5) & 4(-1)-3(1) & 4(2)-3(7) \end{bmatrix}$$

$$=\begin{bmatrix} 34 & 5 & 44\\ 57 & 6 & 69\\ 1 & -7 & -13\\ \end{bmatrix}$$