Let P2 be the vector space of all polynomials ofdegree less than or equal to 2.
(i) Show that {x + 1, x2 + x, x ? 1} is a basis forP2.
(ii) Define a transformation L from P2 intoP2 by: L(f) = (xf)' . In other words,L acts on the polynomial f(x) by first multiplying the function byx, then differentiating. The result is another polynomial inP2. Prove that L is a linear transformation.
(iii) Compute the matrix representation of the lineartransformation L above with respect to the basis for P2from the first part of this problem.
