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If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-1)g(-1)+ f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, 9), ||f|l, Ilg|l, and the angle af.g between f(z) and g(1) for f(x) = 2x² + 3x + 4 and g(x) = 3z2 - 5z - 9. (f, g) = ||f|| = l9|| %3D afg =

If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(-1)g(-1)+ f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, 9), ||f|l, Ilg|l, and the angle af.g between f(z) and g(1) for f(x) = 2x² + 3x + 4 and g(x) = 3z2 - 5z - 9. (f, g) = ||f|| = l9|| %3D afg =

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.2: Divisibility And Greatest Common Divisor
Problem 18E
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If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f, 9) = f(-1)g(-1)+ f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, 9). ||f||, ||g||, and the angle af.g between f(x) and g(x) for f(z) = 2x2 + 3x + 4 and g(x) = 3z2 – 5z - 9. (f, g) = || || = llg|| afg =
Transcribed Image Text:If f(1) and g(1) are arbitrary polynomials of degree at most 2, then the mapping (f, 9) = f(-1)g(-1)+ f(0)g(0) + f(3)g(3) defines an inner product in P2. Use this inner product to find (f, 9). ||f||, ||g||, and the angle af.g between f(x) and g(x) for f(z) = 2x2 + 3x + 4 and g(x) = 3z2 – 5z - 9. (f, g) = || || = llg|| afg =
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