2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2a², –1+ r+a², 1 – r + a²}, {1– 3x + 2², 1 – 3r – 20?, 1 – 2x + 32²}. В B' (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x² + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix PB→B'-

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2a², –1+ r+a², 1 – r + a²}, {1– 3x + 2², 1 – 3r – 20?, 1 – 2x + 32²}. В B' (a) Show that B and B' are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x² + 4x – 2 relative to the bases B and B'. (c) Find the transition matrix PB→B'-

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 34E

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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.

Question

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider
{1+x – 20°, –1+ x+x², 1 – x + 2*} ,
{1– 3x + x?, 1 – 3x – 2a², 1 – 2r + 3x²} .
В
B'
(a) Show that B and B' are bases of P2(R).
(b) Find the coordinate matrices of p(x) = 9x2 + 4x – 2 relative to the bases B and B'.
(c) Find the transition matrix PB→B'.
(d) Verify that
[x(p)]E = PB->B' [x(p) B]-

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