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

Let P₂ be the vector space of all polynomials of degree less than or equal to 2.

(i) Show that {x + 1, x² + x, x − 1} is a basis for P₂.

(ii) Define a transformation L from P₂ into P₂ by: L(f) = (xf)' . In other words, L acts on the polynomial f(x) by first multiplying the function by x, then differentiating. The result is another polynomial in P₂. Prove that L is a linear transformation.

(iii) Compute the matrix representation of the linear transformation L above with respect to the basis for P₂ from the first part of this problem.

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Expert Solution

by using definition i was solved this problem

Colby Messinger answered 5 months ago

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