1. The problem statement, all variables and given/known data Hi all. I have two questions (and two attempts) which I hope you can answer. 1) When I have a linear transformation L : V -> W, and I am asked to find the range (image) of this transformation, what is it exactly I am required to do? (I am not given the matrix A that corresponds to this transformation). Is the range simply the set of functions we get from our transformation L(x)? Sadly, my book doesn't give a proper answer. 2) I have four matrices that span out a vector space W. The four matrices are 2x2 matrices, and they are: A_1 = (1 0 , 0 0) - (that is 1 0 in top, 0 0 in bottom). A_2 = (0 1 , 0 0) A_3 = (0 0 , 1 0) A_4 = (0 0 , 0 1). We have another matrix A = (a b , c d) and a linear transformation F : W -> W given by: F(X) = AX-XA, X is a matrix in W. I have to find the matrix for F with respect to the basis W spanned by A_1 .. A_4. What I did was to find F(A_1) up to F(A_4) and then express this result as a linear combination of A_1 to A_4, e.g.: F(A_1) = 0*A_1 - b*A_2 + c*A_3 - 0*A_4. Then (0,-b,c,0)^T is the first column in my matrix. This gives me a 4x4 matrix - is this approach correct? Thanks in advance, sincerely Niles.