Let V = {ao+a1 x+a2 x² | ao, a1, a2 € R} be a vector space of polynomial up to degree three, and p(x) = po+p1 x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= | p(x)q(x) dæ defines an inner product on V and use Gram-Schmidt process to orthog- onalize the vector in the given standard basis for the vector space V and then normalize these vectors to obtain an orthonormal set respectively.

Let V = {ao+a1 x+a2 x² | ao, a1, a2 € R} be a vector space of polynomial up to degree three, and p(x) = po+p1 x+p2 x², q(x) = q0+q1 x+q2 x² e V then show that < p(x), q(x) >= | p(x)q(x) dæ defines an inner product on V and use Gram-Schmidt process to orthog- onalize the vector in the given standard basis for the vector space V and then normalize these vectors to obtain an orthonormal set respectively.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 6AEXP

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