Do 2×2 matrices e₁₁, e₁₂, e₂₁, e₂₂ span the space of all 2×2 matrices?

[Dustinsfl]

e11, e12, e21, and e22 are 2x2 matrices with all zeros except for a one in ij=11, ij =12, ij=21, and ij=22, respectively.

I know how to show if vectors are a spanning set but I don't know what to do about matrices.

Can someone show me how to approach this? Thanks.

 

[talolard]

What is the dimension of the space of 2x2 matrices? What is the dimension of the set you have? Are they linearly independent? What does that mean?