Problem Statement
Find the matrix $X$ such that:
$$2X + \begin{pmatrix} 3 & -1 \\ 0 & 4 \end{pmatrix} = \begin{pmatrix} 7 & 5 \\ 2 & -2 \end{pmatrix}$$
Verified Solution & Marking Scheme
Isolate 2X by subtracting matrix
$$2X = \begin{pmatrix} 7 & 5 \\ 2 & -2 \end{pmatrix} - \begin{pmatrix} 3 & -1 \\ 0 & 4 \end{pmatrix}$$
$$2X = \begin{pmatrix} 7 - 3 & 5 - (-1) \\ 2 - 0 & -2 - 4 \end{pmatrix} = \begin{pmatrix} 4 & 6 \\ 2 & -6 \end{pmatrix}$$
Divide by scalar 2
$$X = \frac{1}{2} \begin{pmatrix} 4 & 6 \\ 2 & -6 \end{pmatrix} = \begin{pmatrix} 2 & 3 \\ 1 & -3 \end{pmatrix}$$