# 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.

## Solutions

##### Expert Solution

by using definition i was solved this problem

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