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]-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and inequalities describe the relationship between two mathematical expressions.
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![2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider
B = {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].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5faa7035-dfc3-479a-b113-31be2ca1585e%2F00d47b03-c0f3-4d84-b704-885208d26afb%2F28s86s_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let P2(R) be the vector space of polynomials over R up to degree 2. Consider
B = {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].
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