Image is attached 1.In the vector space C[-1,1], an inner product is defined by1= f(x)g(x)dx. Given f(x) = 3x + 1 € C[-1,1], find ||f(x)||.Let u and v be orthonormal vectors in R". ||3u +4v||² = ?Find orthonormal vectors that span the same subspace asV₁ = (1, 1, 1, 1),V₂ = (1,2,3,4), and V3 = (4,3,2,1).4Solve the following system by using least square method.2x+y=1x-y = 5-x-2y = 42.3.

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Answered: 1. In the vector space C[-1,1], an…

1. In the vector space C[-1,1], an inner product is defined by =f(x)(x)dx. Given f(x) = 3x + 1 € C[-1, 1), find ||f(x)||. =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 33EQ

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Question

Image is attached

1.
In the vector space C[-1,1], an inner product is defined by
1
<f,8>= f(x)g(x)dx. Given f(x) = 3x + 1 € C[-1,1], find ||f(x)||.
Let u and v be orthonormal vectors in R". ||3u +4v||² = ?
Find orthonormal vectors that span the same subspace as
V₁ = (1, 1, 1, 1),V₂ = (1,2,3,4), and V3 = (4,3,2,1).
4
Solve the following system by using least square method.
2x+y=1
x-y = 5
-x-2y = 4
2.
3.

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