Question

Solve the matrix equation

Answer 1

AX = C
Matrix A has form 2 x 2
C has form 2 x 2
So, The matrix X must have the form 2 x 2.
Let \[X = \begin{bmatrix}
a & b\\
c & d
\end{bmatrix}\]. If we multiply
\[\begin{bmatrix}
-7 & -3\\
2 & 1
\end{bmatrix}* \begin{bmatrix}
a & b\\
c & d
\end{bmatrix} = \begin{bmatrix}
-7a-3c & -7b-3d\\
2a+c & 2b+d
\end{bmatrix}\] \[ \begin{bmatrix}
-7a-3c & -7b-3d\\
2a+c & 2b+d
\end{bmatrix} = \begin{bmatrix}
2 & 6\\
6 & 9
\end{bmatrix}\] Equating the terms on LHS with corresponding terms on RHS,
-7a - 3c = 2 -7b - 3d = 6
2a + c = 6 2b + d = 9

Solve these two systems of equations

Answer 2

Wow thats alot ok thanks