Consider the linear transformation T : P2 -> P1 specified by T(a0 + a1x +

a2x^2) = (-3a0 + 14a1 - 6a2) + (a0 - 4a1 + 2a2)x.

(a) Write this an equivalent mapping from R^3 to R^2.

(b) Using your answer to (a) or otherwise, specify the standard matrix

representation of T.

(c) The set D = {-3 + x; 7 - 2x} is also a basis for P1. Write down the

transition matrix PS;D, where S1 is the standard basis for P1, and use

it to calculate the transition matrix PD;S.

(d) Calculate the matrix [T]D;S2.

Any help is much appreciated,

Dranalion