(Coordinate systems, basis) Let V be the vector space P2 of polynomials of degree at most 2. (a) Use coordinate vectors to verify that the set B = {1, (t-1), (t-1)2} forms a basis of P2. (b) Use coordinate vectors to verify that the set C = {1, (t + 1), (t + 1)²} forms a basis of P2. (c) What are the coordinate vectors of 1, t + 1 and (t + 1)2 relative to B? (d) Find a matrix P such that for any polynomial f € P2, we have P[f]B = [f]c.
(Coordinate systems, basis) Let V be the vector space P2 of polynomials of degree at most 2. (a) Use coordinate vectors to verify that the set B = {1, (t-1), (t-1)2} forms a basis of P2. (b) Use coordinate vectors to verify that the set C = {1, (t + 1), (t + 1)²} forms a basis of P2. (c) What are the coordinate vectors of 1, t + 1 and (t + 1)2 relative to B? (d) Find a matrix P such that for any polynomial f € P2, we have P[f]B = [f]c.
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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Part d please
![(Coordinate systems, basis) Let V be the vector space P2 of polynomials of degree at most 2.
(a) Use coordinate vectors to verify that the set B = {1, (t− 1), (t− 1)²2} forms a basis of P2.
(b) Use coordinate vectors to verify that the set C = {1, (t + 1), (t + 1)²} forms a basis of P2.
(c) What are the coordinate vectors of 1, t + 1 and (t + 1)2 relative to B?
(d) Find a matrix P such that for any polynomial ƒ € P2, we have P[f]B = [f]c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee563bfe-badf-4a9d-9a7e-d47066dc4e0e%2F67f3d5f9-9f80-40e9-95da-daaebda7235d%2Fzybett9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Coordinate systems, basis) Let V be the vector space P2 of polynomials of degree at most 2.
(a) Use coordinate vectors to verify that the set B = {1, (t− 1), (t− 1)²2} forms a basis of P2.
(b) Use coordinate vectors to verify that the set C = {1, (t + 1), (t + 1)²} forms a basis of P2.
(c) What are the coordinate vectors of 1, t + 1 and (t + 1)2 relative to B?
(d) Find a matrix P such that for any polynomial ƒ € P2, we have P[f]B = [f]c.
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