I'm gonna go ahead and blame lack of sleep as the reason to why I can't do this, lol.
Ok, so I have a set of three 2 x 2 Matrices:
|1 1|, |1 0|, |0 1|
|0 0|, |0 1|, |0 1|
I've got to show that this set is a basis of W where W is defined as a Vector space of upper-triangular 2 x 2 real matrices.
So the first thing I need to do is check to see if the matrices are linearly independent. So would I be right in comparing each matrix with the zero matrix and seeing if the only result obtained is the trivial solution? If so, can I just substitute the ones for a and b? Or do I have to split the matrices into column vectors and give them standard scalar variables? This is where I get confused, preparing the proof.
The next thing I guess would be to show that they span the space, so doing like I did when checking independence, except comparing them to [x,y].
My apologies for not wording this as well as I could have. I'm kinda in a state of confusion, haha.