(k) This question helps you understand linear map i. Suppose b, c E R. Define T : R3 - R2 by T(x, y, z) = (2x - 4y + 3z + b, 6x + cryz). A. show that T is linear map if and only if c = b = 0. B. Can you find the matrix representation of T, if c = b = 0. C. Find the range and kernel of T, if c = b = 0. ii. Can you give an example of an isomorphism mapping from R3 to P2 (R) ? (1) Let A, BE Maxn, where n is an integer greater than 1. Is true that det( A + B) = det(A) + det(B) If so, then give a proof. If not, then give a counterexample. (m) Let A E M3x3 and a, y, Z E R3 and they are linearly independent. Suppose that we have AT = Then find the value of the determinant of the matrix A. (n) Let O O A = 5 6 , B OO 0 9 O Then find the value of det ( A2 B-1 A-2B2 )