How do I show that this is a direct sum? $U$ and $V$ are vector spaces.
$m_1 = \begin{pmatrix}1&0\\0&0\end{pmatrix}$,
$m_2 = \begin{pmatrix}0&0\\0&1\end{pmatrix}$,
$m_3 = \begin{pmatrix}0&1\\1&0\end{pmatrix}$ is a basis of $U$.
And:
$p_1 = \begin{pmatrix}0&1\\-1&0\end{pmatrix}$ is a basis of $V$.
How do I show that $U + V$ is a direct sum?

I'm learning linear algebra, so I want to apologize for any mistakes.
Also, just got into math.stackexchange, so I'm still picking up the formatting.
Thanks in advance.

Let $q \in U \cap V$, then there are scalars $t_1,...,t_4$ such that
$$q=t_1m_1+t_2m_2+t_3m_3=t_4p_1.$$
This gives a system of four linear equations for $t_1,...,t_4$ .
Solve this system and look what happens....
