Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x - 1. Then the set of functions {f, g, h} is abasis for P2, the set of all polynomial functions of degree less than or equal to two.Express the function A(x) = -10x² - 3x - 5 as a linear combination of these basis functions:A = c₁fc29+ c3h.C1 =C2=C3 = Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector off(x) = −4x³ + 3x² - 9x - 8 relative to B.fB =

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Answered: Let B = = (1, x, x², x³) be an ordered…

Let B = = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of f(x) = −4x³ +3x² - 9x - 8 relative to B. fB = 3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 7E

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Question

Suppose that f(x) = x² + 1, g(x) = x² - x and h(x) = x - 1. Then the set of functions {f, g, h} is a
basis for P2, the set of all polynomial functions of degree less than or equal to two.
Express the function A(x) = -10x² - 3x - 5 as a linear combination of these basis functions:
A = c₁fc29+ c3h.
C1 =
C2=
C3 =

Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector of
f(x) = −4x³ + 3x² - 9x - 8 relative to B.
fB =

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