please send handwritten solution for part a Q11 (a) Consider the inner product on P2 defined by(p, q) = aobo + 2a¡b1 + 3azb2for each polynomial p(x) := ao + a1x + a2x² E P2 and q(x) = bo + b1x + b2x² € P2.Using this inner product, find the(i) distance between p(x) = 3 – x + 2x2 and q(x) = 1+ 2x + x²,(ii) angle between p(x) = 3 – x + 2x² and q(x) = 1+2x + x²,(iii) set of all polynomials that are orthogonal to q(x) = 1+ 2x + x².(b) Let V be a real vector space and u, v E V. Show that for every inner product defined onV, u+ v is orthogonal to u – v if ||u|| = ||v||.

Answered: Image /qna-images/answer/e002bcd5-de76-40d6-8daf-995b878a3ce7.jpg

(a) Consider the inner product on P2 defined by (p, q) = aobo + 2a¡b1 + 3azb2 for each polynomial p(x) : = ao + a1x + a2x² E P2 and q(x) = bo + b1x + b2x² E P2. Using this inner product, find the (i) distance between p(x) = 3 - x + 2x2 and q(x) = 1+ 2x + x2, (ii) angle between p(x) = 3 – x + 2x2 and q(æ) = 1+ 2x + x², (iii) set of all polynomials that are orthogonal to q(x) = 1+ 2x +x².

(a) Consider the inner product on P2 defined by (p, q) = aobo + 2a¡b1 + 3azb2 for each polynomial p(x) : = ao + a1x + a2x² E P2 and q(x) = bo + b1x + b2x² E P2. Using this inner product, find the (i) distance between p(x) = 3 - x + 2x2 and q(x) = 1+ 2x + x2, (ii) angle between p(x) = 3 – x + 2x2 and q(æ) = 1+ 2x + x², (iii) set of all polynomials that are orthogonal to q(x) = 1+ 2x +x².

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...

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