Consider the vectorsin R³, and let W be the subspace span{₁, 2}.(a) Find an orthogonal basis for W.3(b) Find the orthogonal projection of y = 1 onto W.10(c) Find the distance from y to (the closest point in) W.25*-8--8== For part (a), note first that the vectors 7₁ and 2 are linearly independent: there are two of them andneither is a scalar multiple of the other. Gram-Schmidt then produces the orthogonal basis {₁, 2} =2{GB]}For part (b), the orthogonal projection formula gives3y-v₂projwy =-U₁ +-9/2V₁ V102 - 029/2Finally, for part (c), the distance is || - projwy|| = || |11/2| || = ¹1211/2-√₂=

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Answered: Consider the vectors R³, and let W be…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 43EQ

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Consider the vectors R³, and let W be the subspace span{1, 2}. a) Find an orthogonal basis for W. 3 o) Find the orthogonal projection of 7 = 1 onto W. 10 5 = --8-8