By justifying your answer determine whether the function is a linear transformation. (a) T : R2 R3, T (x, y) = (x y, 0, xy). (b) T : Mn,n Mm,m, T(A) = XAXT , where X Mm,n is a fixed matrix. (c) T : Mn,n R, T(A) = |XA|, where X Mn,n is a fixed matrix. (d) T : M2,2 P3, T(A) = abx3 2bx2 + cx d, where A = a b c d . (e) T : P2 M2,2, T ax2 + bx + c = a b b c a c . (f) T : P2 P1, T ax2 + bx + c = abcx + (a + b + c) x