Explanation Given: The matrix U = [ a b c 0 d e 0 0 f ] Proof: Case 1: If a = 0, then U = [ 0 b c 0 d e 0 0 f ] We can see that column 1 is 0 and any set of vectors containing 0 is dependent. Case 2: If d = 0, a ≠ 0 then U = [ a b c 0 0 e 0 0 f ] b a [ a 0 0 ] = [ b 0 0 ] We can see that the columns are dependent

Introduction to Linear Algebra, Fifth Edition

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ISBN: 9780980232776

Author: Gilbert Strang

Publisher: Wellesley-Cambridge Press

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Chapter 3.4, Problem 3PS

To determine

To Prove:

If a = 0 or d = 0 or f = 0 ( 3 cases ), the columns of U are dependent

U = [a b c0 d e0 0 f]

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Chapter 3.4, Problem 2PS

Chapter 3.4, Problem 4PS

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Chapter 3 Solutions

Introduction to Linear Algebra, Fifth Edition

Ch. 3.1 - Prob. 1PS Ch. 3.1 - Prob. 2PS Ch. 3.1 - Prob. 3PS Ch. 3.1 - Prob. 4PS Ch. 3.1 - Prob. 5PS Ch. 3.1 - Prob. 6PS Ch. 3.1 - Prob. 7PS Ch. 3.1 - Prob. 8PS Ch. 3.1 - Prob. 9PS Ch. 3.1 - Prob. 10PS

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