D: P2> P2 (Dthe differential operator so that D(ax²+bx+c) = 2ax +b); a the standard basis for P2; B the basis consisting of x2+1, x+1, 2x2+1; ở = x² + 2x – 2. d) Find [T]. e) Find [v]g for i = x2 + 2x – 2. f) Find [T(v)]g.

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Using linear algebra, show that G={p1(x)=1−x+x^2, p2(x)=x, p3(x)=x+x^2} is a basis of P2, the vector space of polynomials of degree at most two with real coefficients.

Compute the quadratic form x' Ax for A = X1 5 444 X2 -9 x3 a. x = a. x¹ Ax= b. x' Ax= C. X' Ax= 1/√√3 b. x= 7 C. X = - 1/√3 1/√√3 (Simplify your answer.) 360 643 035 (Simplify your answer.) and each of the following vectors.