a) Find a base for $W_1 \cap W_2$ and b) Find a base for $W_1 + W_2$ Let 
$$W_1 = \left\{ \begin{pmatrix}
    a & b & c \\
   -b & a & b \\
    c & b & a \\
\end{pmatrix} :\, a, b, c \in \Bbb R \right\}$$
$$W_2 = \left\{
    \begin{pmatrix}
    a & 0 & 0 \\
    b & 0 & c \\
    c & b & a \\
\end{pmatrix} :\, a, b, c \in \Bbb R \right\}$$
a) Find a basis for $W_1 \cap W_2$
b) Find a basis for $W_1 + W_2$
For a) I`m  not sure if the set for $W_1 \cap W_2 = $ $ \{
    \begin{pmatrix}
    0 & 0 & 0 \\
    0 & 0 & 0 \\
    0 & 0 & 0 \\
    \end{pmatrix}\} 
$ 
so the base is only the zero matrix.
For b) I belive the set is: $W_1 + W_2 = $ $ \{
    \begin{pmatrix}
    2a & b & c \\
    0 & a & b+c \\
    2c & 2b & 2a \\
    \end{pmatrix}
$:$ a, b, c \in R\}$
But don`t know how to give an 
appropriate base for this set. 

a) Since $W_1\cap W_2=\{0\}$, the only basis of $W_1\cap W_2$ is the empty set.
b) Since $W_1\cap W_2=\{0\}$, a way of finding a basis $B$ of $W_1+W_2$ is to take a basis $B_1$ of $W_1$ and a basis $B_2$ of $W_2$ and then to take $B=B_1\cup B_2$. It is natural to take$$B_1=\left\{\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix},\begin{bmatrix}0&1&0\\-1&0&1\\0&1&0\end{bmatrix},\begin{bmatrix}0&0&1\\0&0&0\\1&0&0\end{bmatrix}\right\}$$and$$B_2=\left\{\begin{bmatrix}1&0&0\\0&0&0\\0&0&1\end{bmatrix},\begin{bmatrix}0&0&0\\1&0&0\\0&1&0\end{bmatrix},\begin{bmatrix}0&0&0\\0&0&1\\1&0&0\end{bmatrix}\right\}.$$
