Let D be the vector space of all differentiable functions mapping R into R. Let V be the subspace of D defined by V = sp(x? e* , xe* , e* ). Define the linear transformation T: V –V by T(f) =f*the derivative of f. Let ordered bases for V be B = B' = (x² e*, xe", e* ). Find the matrix representation A of T relative to B, B’. Then use A to compute T(f), where f(x) = 3x² ex – 4xe* + 2e*.

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A: This is a problem of linear transformation.

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A: Solution of the problem as follows

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.