I'm trying to determine whether [the set of all 2x2 matrices] is in the span of the following matrices:
1 0
0 1
0 1
0 0
0 0
1 0
0 0
0 1
If a basis for [the set of all 2x2 matrices] is in the span of these four matrices, then does the set of matrices span [the set of all 2x2 matrices]? Also, is there a faster way to determine whether the set spans [the set of all 2x2 matrices]?