The set $W$ is a subspace of $M_{22}$, the vector space of all $2\times 2$ matrices. Prove that $S$ is a spanning set for $W$. \begin{align*} W&=\setparts{\begin{bmatrix}a&b\\c&d\end{bmatrix}}{2a-3b+4c-d=0} & S=&\set{ \begin{bmatrix}1&0\\0&2\end{bmatrix},\, \begin{bmatrix}0&1\\0&-3\end{bmatrix},\, \begin{bmatrix}0&0\\1&4\end{bmatrix} } \end{align*}