Solution MO.C11 Chris Black

The given equation \begin{align*} \begin{bmatrix} -1 & 1 & 0 \\ 0 & 5 & -2 \end{bmatrix} &= 2\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 2 \end{bmatrix} - 3\begin{bmatrix} 1 & 1 & 2 \\ 0 & 1 & x \end{bmatrix} = \begin{bmatrix} -1 & 1 & 0 \\ 0 &5 & 4 - 3x \end{bmatrix} \end{align*} is valid only if $4 - 3x = -2$. Thus, the only solution is $x = 2$.