The linear transformation L defined by L(p(x)) = p_ (x) + p(0) maps P3 into P2. Find the

Chapter 4, Problem 14

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The linear transformation L defined by L(p(x)) = p_ (x) + p(0) maps P3 into P2. Find the matrix representation of L with respect to the ordered bases [x2, x, 1] and [2, 1 x]. For each of the following vectors p(x) in P3, find the coordinates of L(p(x)) with respect to the ordered basis [2, 1 x]: (a) x2 + 2x 3 (b) x2 + 1 (c) 3x (d) 4x2 + 2x 1

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