use the Gram-Schmidt algorithm to convertthe base {1, X, X²} space to an orthogonalbase where the internal Product isOP, Q = P(o) Q (0) + P(1) Q (1) + P (2) Q (2)2Ⓒ Q >= √ ² P(x) Q (x) dx2

Answered: 2 Gram-Schmidt algorithm to conv -e {1,…

2 Gram-Schmidt algorithm to conv -e {1, x, x} space to an orthogo where the internal Product is => = P(0) Q (0) + P(1) Q (1) + P (2) Q = •>=S² P(x) Q (x) dx

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section: Chapter Questions

Problem 15RQ

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Question

use the Gram-Schmidt algorithm to convert
the base {1, X, X²} space to an orthogonal
base where the internal Product is
O
P, Q = P(o) Q (0) + P(1) Q (1) + P (2) Q (2)
2
Ⓒ <P> Q >= √ ² P(x) Q (x) dx
2

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