Determining vector space basis

Question

I am required to find the basis of : $$ M=\left\{\begin{bmatrix}m & m \\2m & 0 \end{bmatrix} : m \in\Bbb R\right\} $$ Now I am aware of the process when I have two different elements of the matrix, (for example a and b), what I am interested in is how can I make multiple linearly independent vectors that correspond to this exact space ?

Thanks in advance.

Answer 1

Did you notice that every matrix in this set if of the form $m\begin{bmatrix}1 & 1 \\ 2 & 0 \end{bmatrix}$? So every matrix is a multiple of $\begin{bmatrix}1 & 1 \\ 2 & 0 \end{bmatrix}$.

(Thanks, amsmath.)