I have this question:
The dimension of the vector subspace $W$ of $M_2(\Bbb C)$ given by
$W = \left\{\begin{pmatrix}a&b\\c&d\\ \end{pmatrix}: a, b, c, d\in\Bbb C, a + b = c, b + c = d, c + a = d\right\}$ is equal to ....
I took this approach: we see that $a=b$, and $c=2a$ and $d=3a$, so, $W$ consists of matrices $\begin{pmatrix}a&a\\2a&3a\\ \end{pmatrix}$, hence dimension is 1. Am I right?