Basis and dimension of Matrices

Hello, first time posting on the forum. Been here a lot in my past couple of semesters with homework help. I've browsed as much as I could for help on this problem but I haven't made any advancement. Any help would be greatly appreciated.

The problem reads

Find a basis and the dimension of the subspace W of V = , spanned by

.

TBH I barely have any idea where to start here. I understand bases and I can do them when they involve 1x1 vectors, but these are 2x2 and have no idea how to set it up. TIA

DP