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10 Nov 2019
Let T: P2(R) rightarrow P3(R) be the linear transformation defined by T p(x) = xp(x). Consider the bases alpha = {1 - x, 1 - x2, x} for P2(R) and beta = {1, 1 + x, 1 + x + x2, 1 - x3} for P3(R) Use [T]beta alpha to find a basis for the image of T.
Let T: P2(R) rightarrow P3(R) be the linear transformation defined by T p(x) = xp(x). Consider the bases alpha = {1 - x, 1 - x2, x} for P2(R) and beta = {1, 1 + x, 1 + x + x2, 1 - x3} for P3(R) Use [T]beta alpha to find a basis for the image of T.