Exercise 5 Consider 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-...

Extracted text: Exercise 5 Consider 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 its matrix M(p) in the basis r + r², 2² – 1,r + 5 of P2(R). %3D