(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 e P2, we have P[f]B = [f]c. (e) Answer TRUE, FALSE or NONSENSE:

(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 e P2, we have P[f]B = [f]c. (e) Answer TRUE, FALSE or NONSENSE:

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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