Show subspaces of two matrices Let$ V = M_2(\Bbb R)$ and let

$$W_1=\{
        \begin{pmatrix}
        x & -x  \\
        y & z \\
        \end{pmatrix}
x,y,z\in \Bbb R
\}
$$ and 
$$W_2=
\{
        \begin{pmatrix}
        a & b  \\
        -a & c \\
        \end{pmatrix}
a,b,c\in \Bbb R
\}
$$
 Show that W1 and W2 are subspaces of V and find a basis for W1 + W2. Is
this sum direct?
How do I show they're subspaces? I know what subspaces are and how to show them in general i.e. it is a non empty set that and u+av is an element of that set where u,v are elements of the set and a is a scalar of the vector space. What I'm stuck on is how to apply that in this scenario.

Hint: Clearly the zero matrix belongs to both $W_1$ and $W_2$, so both of them are non-empty. Taking $A$ and $B$ from $W_1$ (respectively from $W_2$), it is easy to see that for any scalar $c$, $A+cB$ is in $W_1$ (respectively in $W_2$): say $A=\begin{pmatrix}
x_1&-x_1\\
y_1&z_1
\end{pmatrix}\in W_1$ and 
$B=\begin{pmatrix}
x_2 & -x_2\\
y_2& z_2
\end{pmatrix}\in W_1$, then for any scalar $c$ we have $A+cB=\begin{pmatrix}
x_1+cx_2& -(x_1+cx_2)\\
y_1+cy_2&z_1+cz_2
\end{pmatrix} \in W_1$ and similarly for $W_2$.
The sum $W_1+W_2 $ is not direct as $W_1\cap W_2=\left\{\begin{pmatrix}
a&-a\\
-a &b
\end{pmatrix}:a,b\in\Bbb R\right\}$ , in particular $\begin{pmatrix}
0&0\\
0&1
\end{pmatrix}\in W_1\cap W_2$. Also note that the dimension of both of $W_1$ and $W_2$ are $3$ and that of $W_1\cap W_2$ is $2$.
