Let S: M_n(R) -> M_n(R) defined by: S(A) = A - A^T
Now, I need to do three things for this question. a) Show S is a linear transformation b) Find Ker(S) and describe it c)) Find Rng(s) and describe it
For part a, i just showed that S(A)=A-A^T satisfies addition and scalar multiplication, which wasn't too difficult of a task. For addition, i made S(A+B) = (A+B) - (A+B)^T then worked out the algebra till i got S(A+B) on the right side of the equation. For scalar multiplication id di the same thing with S(cA) = cA-cA^T.
I am not sure how to start the second 2 sections though (b&c). I know how to get the kernel (nullspace) of a matrix, but not for a question like this. Can anyone help me?