I have dosed off in class way too many times and I need help with a few problems from my pre-test:
Prove that M_22 is isomorphic to P_3.
A simple hint in the right direction would be greatly appreciated.
The matrix you are mapping from is 2-by-2, and I was presuming the OP was getting confused by the linear map ~ matrix equivalence (it seemed like he was trying to find the kernel of the 2-by-2 matrix). That is why I wanted to point out that T is 4-by-4.