15.Let S be the subspace of R° spanned by the vectors1and224. Find the matrix P for the orthogonal projection onto S.(If the entries of your matrix do not come out as whole numbers, roundthem to 4 decimal places.) Let V[2, 1, 8] and U = [3, 2, 9]. Find a scalar c such thatV – CU is orthogonal to U. Give an exact answer, not a decimalapproximation.|с —

By Bartleby policy I have to solve only first one as these 2 are unrelated problems.

Answered: -1-日 5 Let S be the subspace of R°…

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 7EQ

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-1-日 5 Let S be the subspace of R° spanned by the vectors and 2 2 . Find the matrix P for the orthogonal projection onto S. (If the entries of your matrix do not come out as whole numbers, round them to 4 decimal places.)