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SOLVED: Let P2 be the vector space of polynomials in x of degree 2 or less.(a) Let W be the linear subspace of P2 spanned by p1(x) = 1 x^2, p2(x) = 2 2x - x^2, and p3(x) = 1 6x - 8x^2. Find a basis for W.(b) Let T: P2 → R2 be the linear transformation defined by T(p) = (p(3), p'(3)), where p'(x) denotes the derivative of p(x). Find a matrix for T relative to the basis B = 1, x, x^2 of P2 and the standard basis e1, e2 of R2.
SOLVED: Let P2 be the vector space of polynomials in x of degree 2 or less.(a) Let W be the linear subspace of P2 spanned by p1(x) = 1 x^2, p2(x) = 2 2x - x^2, and p3(x) = 1 6x - 8x^2. Find a basis for W.(b) Let T: P2 → R2 be the linear transformation defined by T(p) = (p(3), p'(3)), where p'(x) denotes the derivative of p(x). Find a matrix for T relative to the basis B = 1, x, x^2 of P2 and the standard basis e1, e2 of R2.
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