2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x = 2a°, –1+ x + a*, 1 – x + a²} , B' = {1- 3x + a², 1 – 3x – 20², 1 – 2x + 3a²}. (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(r) = 9x² + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix Pg→B'. (d) Verify that [x(p)]B = PB-¬B' [x(p)B].

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: 2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x*, –1+x…

A: The solution is given as follows :

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A: This question is about application of linear algebra

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Q: 3c

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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.