Extend the basis of subspace $U$ to the basis $M_{2 \times 2}^{\mathbb R}$ by adding vectors from the standard basis of $M_{2 \times 2}^{\mathbb R}$

Question

Extend the basis of subspace $U$ to the basis $M_{2 \times 2}^{\mathbb R}$ by adding vectors from the standard basis of $M_{2 \times 2}^{\mathbb R}$. The basis of $U$ is $B_U=\{\begin{pmatrix}1&2\\4&1\end{pmatrix},\begin{pmatrix}0&3\\1&-1\end{pmatrix}\}$.

Could I say that the problem is equivalent to finding the subspace $T$ such that $M_{2 \times 2}^{\mathbb R}=U \oplus T$?