(2) Give an example of each of the following: (a) A matrix Q that has orthonormal columns but QQT + I. (b) Two orthogonal vectors that are not linearly independent. 1 (c) An orthonormal basis for R³, including the vector q1 = 1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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(2) Give an example of each of the following:
(a) A matrix Q that has orthonormal columns but QQ" I.
(b) Two orthogonal vectors that are not linearly independent.
1
(c) An orthonormal basis for R³, including the vector q1 = | 1
V3
Transcribed Image Text:(2) Give an example of each of the following: (a) A matrix Q that has orthonormal columns but QQ" I. (b) Two orthogonal vectors that are not linearly independent. 1 (c) An orthonormal basis for R³, including the vector q1 = | 1 V3
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