Question

Consider T : R 3 → R 3 defined by T(x, y, z) = (2x − 3y + 5z, x− 4y − 4z, 9x + 5y + z). (a) (2 marks) Recall that AS, the matrixfor T with respect to the standard basis S = {e1, e2, e3} has ithcolumn equal to Tei . Write down AS. (b) (2 marks) write down P,the change of basis matrix from B = {(1, 2, 7),(−2, 3, 5),(2, 2,17)} to the standard basis S. You do not have to prove that B is abasis of R 3 here, but should be able to do so if required. (c) (2marks) Express AB, the matrix for T with respect to the basis B ofpart (b), as the product of three matrices