ker T is the set of all x such that Tx=0. Finding that isomorphism is one way to do it, but not the only one. Edit: Wait, you said "from T[a,b;c,d]". I don't know what you mean by that. I meant that one way to solve the problem is to find an isomorphism from the set of 2×2 matrices to ℝ^{4}.So what does ker(T) stand for? Im still really clueless. So do I find an isomorphism from T[a,b;c,d] to (a,b,c,d)?
I guess I wasn't much clear. What I meant is that T takes a matrix [a,b;c,d] and gives a vector (a,b,c,d). Actually, I think that this is what he has meant.ker T is the set of all x such that Tx=0. Finding that isomorphism is one way to do it, but not the only one. Edit: Wait, you said "from T[a,b;c,d]". I don't know what you mean by that. I meant that one way to solve the problem is to find an isomorphism from the set of 2×2 matrices to ℝ^{4}.