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) x 2 + 2x − 3
(b) x 2 + 1
(c) 3x
(d) 4x2 + 2x
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