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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 2RQ

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Question

Determine, with justification, whether the following sets are subspaces of R4.
--|
I4 = 0
(a) S
(b) S
(c) S =
1
12
13
I4
IL
12
13
IA
I
1²
Y
12
ER¹ : : x1 + x₂ - 13
ER¹₁+ |₂|-|T3|-|T4|=
-o}.
ER¹ :1, y ER

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Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
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