Question #275329

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



1
Expert's answer
2021-12-07T11:28:12-0500
A=[312513],B=[412517]A=\begin{bmatrix} 3 & -1 & 2\\ 5 & 1& 3 \end{bmatrix}, B=\begin{bmatrix} 4 & -1 & 2\\ 5 & 1 & 7 \end{bmatrix}

C=[163943]C=\begin{bmatrix} 1 & 6\\ 3 & 9 \\ 4 & -3 \end{bmatrix}

i.


3A=[9361539]3A=\begin{bmatrix} 9 & -3 & 6\\ 15 & 3 & 9 \end{bmatrix}

2B=[82410214]2B=\begin{bmatrix} 8 & -2 & 4\\ 10 & 2 & 14 \end{bmatrix}


ii.


3A2B=[112515]3A-2B=\begin{bmatrix} 1 & -1 & 2\\ 5 & 1 & -5 \end{bmatrix}

iii.


CB=[163943][412517]CB=\begin{bmatrix} 1 & 6\\ 3 & 9 \\ 4 & -3 \end{bmatrix}\begin{bmatrix} 4 & -1 & 2\\ 5 & 1 & 7 \end{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)]=\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}

=[34544576691713]=\begin{bmatrix} 34 & 5 & 44\\ 57 & 6 & 69\\ 1 & -7 & -13\\ \end{bmatrix}


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