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Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 + (−6) x + (−5) x², −7 + 7x + (−9) x²) 2) ||−4 + (−6) x + (−5) x² || = 3) The distance between −4+ (-6) x + (-5) x² and -7 + 7x + (-9) x² is: 4) A value of a that would allow for 1 + ax and -4+ (-6) x + (-5) x² to be orthogonal would be:

Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 + (−6) x + (−5) x², −7 + 7x + (−9) x²) 2) ||−4 + (−6) x + (−5) x² || = 3) The distance between −4+ (-6) x + (-5) x² and -7 + 7x + (-9) x² is: 4) A value of a that would allow for 1 + ax and -4+ (-6) x + (-5) x² to be orthogonal would be:

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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answer no. 4 only plesse

Note: To use square roots, you can simply write "a^0.5". Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4+ (−6) x + (−5) x², −7+ 7x + (-9) x²) 2) ||−4+ (−6) x + (−5) x²|| = 3) The distance between −4+ (-6) x + (-5) x² and −7+ 7x + (-9) x² is: 4) A value of a that would allow for 1 + ax and −4+ (−6) x + (−5) x² to be orthogonal would be:
Transcribed Image Text:Note: To use square roots, you can simply write "a^0.5". Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4+ (−6) x + (−5) x², −7+ 7x + (-9) x²) 2) ||−4+ (−6) x + (−5) x²|| = 3) The distance between −4+ (-6) x + (-5) x² and −7+ 7x + (-9) x² is: 4) A value of a that would allow for 1 + ax and −4+ (−6) x + (−5) x² to be orthogonal would be:
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