How do I put $$\left[ \begin{matrix} 2&0&0 \\ 0&-1&0 \\ 0&0&1 \end{matrix}\right]$$ and $$\left[\begin{matrix} -2&0&0\\ 0&-1&0\\ 0&0&-1 \end{matrix}\right]$$
into a single matrix?
I'm trying to find the span and check whether is it linearly independent. I do understand to find both I need it to be in a single matrix but I'm a little confused on how to get started.
A little help would be much appreciated. Thank you! :)
Hint: $$ \alpha\begin{bmatrix} 2&0&0 \\ 0&-1&0 \\ 0&0&1 \end{bmatrix} +\beta\begin{bmatrix} -2&0&0\\ 0&-1&0\\ 0&0&-1 \end{bmatrix}= \begin{bmatrix} 0&0&0\\ 0&0&0\\ 0&0&0 \end{bmatrix} $$ implies what about $\alpha$ and $\beta$?