Exercise 5Consider P2(R), the space of quadratic polynomials with real coef-ficients.a) Show that r + x², a² – 1, r +5 is a base of P2(R).b) For each of the polynomial p = 2 +2r + 5x2, r2- 2r-7,2r2 - 7r 29, find itsmatrix M(p) in the basis r + r², 2² – 1,r + 5 of P2(R).%3D

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Exercise 5 Consider P2(R), the space of quadratic polynomials with real coef- ficients. a) Show that r + x²,x² – 1, r + 5 is a base of P2(R). b) For each of the polynomial p = 2+ 2x + 5x2, a-2x- 7, 2r2 - 7r 29, find its matrix M(p) in the basis r+ r², r² - 1,r + 5 of P2(R). %3D

Exercise 5 Consider P2(R), the space of quadratic polynomials with real coef- ficients. a) Show that r + x²,x² – 1, r + 5 is a base of P2(R). b) For each of the polynomial p = 2+ 2x + 5x2, a-2x- 7, 2r2 - 7r 29, find its matrix M(p) in the basis r+ r², r² - 1,r + 5 of P2(R). %3D

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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