Answer to Question #338501 in Linear Algebra for Nick

Question

Linear transformation T : P2 → P2, T(a+bx+cx2 ) = (2a−b)+(a+b−3c)x+(c−a)x 2

a. Find the matrix representation A of T with respect to the ordered bases B = {1, x + 1, x2 + 1} and B0 = {1, x, x2}.

b. Let q(x) = a + bx + cx2 ∈ P2. Verify that A[q(x)]B = [T(q(x))]B'.

Answer 1

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