Answer:
Option (2)
Step-by-step explanation:
Given expression is, AX + B = C
[tex]A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}[/tex]
[tex]B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}[/tex]
AX + B = C
AX = C - B
C - B = [tex]\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}[/tex] = [tex]\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}[/tex]
C - B = [tex]\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}[/tex]
Let [tex]X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex]
AX = [tex]\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}\times \begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}[/tex]
Since AX = C - B
[tex]\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}[/tex]
Therefore, a = 1, b = 5
(-3a - 4c) = -35
3(1) + 4c = 35
3 + 4c = 35
4c = 32
c = 8
And (-3b - 4d) = -11
3(5) + 4d = 11
4d = -4
d = -1
Therefore, Option (2). X = [tex]\begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix}[/tex] will be the answer.
