quick question

Seems to me like the most straightforward way to go is to break out the pencil and paper and crank it through. Start with the most generic matrix possible:

X=[x1x2x3x4]\displaystyle X = \begin{bmatrix} x_1 & x_2 \\ x_3 & x_4 \end{bmatrix}

Then do matrix multiplication per the usual rules to end up with two matrices in terms of these unknown parameters, on either side of the equation:

[−22−65]X=[????????]\displaystyle \begin{bmatrix} -2 & 2 \\ -6 & 5 \end{bmatrix}X = \begin{bmatrix} \text{??} & \text{??} \\ \text{??} & \text{??} \end{bmatrix}

[−84−6−5]X=[????????????]\displaystyle \begin{bmatrix} -8 & 4 \\ -6 & -5 \end{bmatrix}X = \begin{bmatrix} \text{???} & \text{???} \\ \text{???} & \text{???} \end{bmatrix}

And finally perform the matrix addition per the usual rules:

[????????]+[6−87−6]=[????????????]\displaystyle \begin{bmatrix} \text{??} & \text{??} \\ \text{??} & \text{??} \end{bmatrix} + \begin{bmatrix} 6 & -8 \\ 7 & -6 \end{bmatrix} = \begin{bmatrix} \text{???} & \text{???} \\ \text{???} & \text{???} \end{bmatrix}

...to create four equations in four unknowns (the parameters x1 ,x2, x3, x4\displaystyle x_1 \:, x_2, \: x_3, \: x_4)
 
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