Solve the marked sub part 2. Let P2(R) be the vector space of polynomials over R up to degree 2. ConsiderB = {1+x – 2a², –1+x + a², 1 – x + x²},B' = {1- 3x + a², 1 – 3x – 2u², 1 – 2x + 3x²} .(a) Show that B and B' are bases of P2(R).(b) Find the coordinate matrices of p(æ) = 9x² + 4x – 2 relative to the bases B and B'.(c) Find the transition matrix Pg-B'.V Verify that[x(p)]B' = PB¬B' [x(p)B].

The solution is given as follows :

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x*, –1+x + a², 1 – x + 2²}, B' = {1- 3x + x², 1 – 3.x – 2a², 1 – 2x + 3x²} . (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'. V Verify that [x(p)]B" = PB-¬B' [x(p)B]-

2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B = {1+x= 2x*, –1+x + a², 1 – x + 2²}, B' = {1- 3x + x², 1 – 3.x – 2a², 1 – 2x + 3x²} . (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'. V Verify that [x(p)]B" = PB-¬B' [x(p)B]-

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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