1) Let P2 = {polynomials f(x) = a2x²+a1x+ao, where ao, a1, a2 E R}, and define addition and scalar multiplication as follows: (a) Addition. Let f(x) = a2x² +a1x +ao and g(x) b2x² +b1x+ bo-. Then define (f + g)(x) = (a2 + b2)x² + (a1 + b1)x + (ao + bo) (b) Scalar multiplication. Let r E R, f(x) = a2x² + a1x + ao. Define (rf)(x) = (ra2)x² + (ra1)x + (rao) Show that P2 is a vector space.

1) Let P2 = {polynomials f(x) = a2x²+a1x+ao, where ao, a1, a2 E R}, and define addition and scalar multiplication as follows: (a) Addition. Let f(x) = a2x² +a1x +ao and g(x) b2x² +b1x+ bo-. Then define (f + g)(x) = (a2 + b2)x² + (a1 + b1)x + (ao + bo) (b) Scalar multiplication. Let r E R, f(x) = a2x² + a1x + ao. Define (rf)(x) = (ra2)x² + (ra1)x + (rao) Show that P2 is a vector space.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 46E

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