Problem:
1. Let T be a linear operator on P_3 defined as follows:
T(ax^3 + bx^2 + cx + d) = (a - b)x^2 + (c - d)x + (a + b - c).
The matrix [T]_G which represents T with respect to the basis G which = {1 + x, 1 - x, 1 - x^2, 1 - x^3}. Show that the standard matrix representation and the preceding matrix representation are similar. Show work.