Let T1: P1 → P2 be the linear transformation defined by
T1(c0 + c1x) = 2c0 - 3c1x
and let T2: P2 → P3 be the linear transformation defined by
T2(c0 + c1x + c2x2) = 3c0x + 3c1x2 + 3c2x3
Let B = (1, x), B′′ = {1, x, x2}, and Bt = {1, x, x2, x3}.
(a) Find [T2 o T1]B′,B, [T2] B′,B′′, and [T1] B′′,B.
(b) State a formula relating the matrices in part (a).