I have a question in which I find a base for $W$, which is $\left \{ \begin{bmatrix} 1 & 1 &1 \\ 1 & 2 & 3 \end{bmatrix},\begin{bmatrix} 0 & -1 &0 \\ 1 & 0 & 0 \end{bmatrix} \right \}$. Later on in the question, I'm asked to find a subspace $T$ such that $\mathbb{M}_{2\times 3}^{\mathbb{R}}=W \oplus T$.
I'm clueless of what I am supposed to do, I know $\dim T=4$ and that $T\cap W=\left \{ 0 \right \}$. But that doesn't assist me much.