1. The problem statement, all variables and given/known data Find the domain, target space, image, rank and nullity of the linear transformation T(A)=Av, where v= (1, 2) and A is any 2×2matrix. 2. Relevant equations 3. The attempt at a solution I believe I know the domain (R2x2 vector space) and target space (R2), but I am not sure how to solve for the image, rank, and nullity. I have tried making the matrix A an arbitrary 2x2 matrix with the variables a, b, c, d but this doesn't seem to be making it easy to find the image or rank. And I think if I am able to find the rank, I can find the nullity based on the rank-nullity theorem.