Question

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Answer 1

Answer:

$X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}$

Step-by-step explanation:

Matrix Equations

Given:

$A=\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}$

$B=\begin{bmatrix}-4 &-3 \\3 &9 \\9 &-4 \end{bmatrix}$

Find X such that:

B - X = 3A

Subtracting B:

- X = 3A - B

Multiplying by -1:

X = -3A + B

Find -3A:

$-3A=-3\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}=\begin{bmatrix}21 &6 \\-27 &-21 \\-6 &-12 \end{bmatrix}$

Add to B:

$X=-3A+B=\begin{bmatrix}21 &6 \\-27 &-21 \\-6 &-12 \end{bmatrix}+\begin{bmatrix}-4 &-3 \\3 &9 \\9 &-4 \end{bmatrix}=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}$

Thus:

$X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}$