Answer:
[tex]X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}[/tex]
Step-by-step explanation:
Matrix Equations
Given:
[tex]A=\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}-4 &-3 \\3 &9 \\9 &-4 \end{bmatrix}[/tex]
Find X such that:
B - X = 3A
Subtracting B:
- X = 3A - B
Multiplying by -1:
X = -3A + B
Find -3A:
[tex]-3A=-3\begin{bmatrix}-7 &-2 \\9 &7 \\2 &4 \end{bmatrix}=\begin{bmatrix}21 &6 \\-27 &-21 \\-6 &-12 \end{bmatrix}[/tex]
Add to B:
[tex]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}[/tex]
Thus:
[tex]X=\begin{bmatrix}17 &3 \\-24 &-12 \\3 &-16 \end{bmatrix}[/tex]
