Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B ={1 + x − 2x^2 , −1 + x + x^2, 1 − x + x^2}, B' ={1 − 3x + x^2, 1 − 3x − 2x^2, 1 − 2x + 3x^2}. (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x^2 + 4x − 2 relative to the bases B and B'. (c) Find the transition matrix P_B=→B'

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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.