Let A and B be nxn matrices. Assume that B is non-singular and set C = BA. (a) Show that N(A) = N(C). (b) Let b ERbe such that the equation Ax = b is consistent, and there exists a non-zero scalar leR for which Bb = \b. Show that the equation Cx = b is consistent. (c) With notation as in part (b), express the solution set of the equation Cx = b in terms of N(A) and a particular solution xo to the equation Ax = b. Let A and B be nxn matrices. Assume that B is non-singular and set C = BA. (a) Show that N(A) = N(C). (b) Let b ERbe such that the equation Ax = b is consistent, and there exists a non-zero scalar leR for which Bb = \b. Show that the equation Cx = b is consistent. (c) With notation as in part (b), express the solution set of the equation Cx = b in terms of N(A) and a particular solution xo to the equation Ax = b