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Let P2 be the vector space of all polynomials of degree less than or equal to...

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Advance Math

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.

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