10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3v} for span(S). Then verify that a Espan(S) can be written in the{0₁, 02,1formI =-1 27kΣ(x, v.)vi.i=1(a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2).(b) V M₂(R) (with Frobenius norm) Sand r = A(c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t},and h(t) = 2t + 1.3-1 9{G) (2) 6_D)}5-1

Since you post non interlinking three questions as per our guideline we can solve only first…

10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form and r = A I = (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S -1 27 k Σ(x, v.)vi. i=1 3 -1 9 {G) (2) 6_D)} 5 -1 (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1.

10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then verify that a Espan(S) can be written in the {0₁, 02,1 form and r = A I = (a) V = R³, S = {(1, 0, 1), (0, 1, 1), (1,3,3)}, and x = (1,1,2). (b) V M₂(R) (with Frobenius norm) S -1 27 k Σ(x, v.)vi. i=1 3 -1 9 {G) (2) 6_D)} 5 -1 (c) V = span(S) with the inner product (f, g) = f(t)g(t) dt, S = {sin t, cost, t}, and h(t) = 2t + 1.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 37EQ

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