[SOLVED] Combined linear transformations 1. The problem statement, all variables and given/known data I have a linear transformation L : R^3 -> R^3 represented by a matrix A. I also have another linear transformation S : R^3 -> R represented by a matrix B. The dimensions of the matrix A must be 3x3 and for B it is 1x3. I have to find the rank and the nullity of the linear transformation S o L. I don't know if it's necessary, but the linear transformations are: L(x,y,z) = (6x-3y-2z , 14x-7y-4z , -5x+3y+3z) and S(x,y,z) = x+y+z. 3. The attempt at a solution The transformation S o L is linear, because S and L is linear and the matrix C that represents S o L is given by B*A. This product gives me a 1x3 matrix and the rank and nullity of this matrix is what is being asked for. But how (or is it even possible) to find the rank and nullity of C? Thanks for all your help, sincerely Niles.