Let W, X, Y and Z be full column rank real matrices. What are the conditions (if any) on W, X, Y and Z, such that there exists a real matrix A such that A X = Z and YT A = W T ? Find all such A when the conditions are satisfied. How many linearly independent equations were there? What was the dimensionality of the left and right nullspaces? Did the rank-nullity theorem hold? The previous exercise can provide a simple way to approach this problem.