A vector space of 2x2 Matrices with real entries, and let A be a subspace defined by

.

How would you go about finding the dimension of A?

(The question I'm looking at does have real entries, but I just want the general idea).

I've missed the lecture on this, but my attempt is to show that they are linearly independent. If they are linearly independent then they form a basis. Then writing it out in a reduced row-echelon form and any rows that do not contain a leading coefficient are redundant and the dimension of A would be the number of rows that do contain a leading coefficient.