Question

Given: A, B, and C What is the value of X in the matrix equation AX + B = C?

Answer 1

the second option is your answer

Explanation:

Answer 2

Option (2)

Explanation:

Given expression is, AX + B = C

`A=\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}`

`B=\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}`

`C=\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}`

AX + B = C

AX = C - B

C - B =
`\begin{bmatrix}-42 & -20\\ 5 & 4\end{bmatrix}-\begin{bmatrix}-7 & -9\\ 4 & -1\end{bmatrix}` =
`\begin{bmatrix}-42+7 & -20+9\\ 5-4 & 4+1\end{bmatrix}`

C - B =
`\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}`

Let
`X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}`

AX =
`\begin{bmatrix}-3 & -4\\ 1 & 0\end{bmatrix}* \begin{bmatrix}a & b\\ c & d\end{bmatrix}`

=
`\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}`

Since AX = C - B

`\begin{bmatrix}(-3a-4c) & (-3b-4d)\\ a & b\end{bmatrix}=\begin{bmatrix}-35 & -11\\ 1 & 5\end{bmatrix}`

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 =
`\begin{bmatrix}1 & 5\\ 8 & -1\end{bmatrix}` will be the answer.