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

5th Edition

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

Ch. 3.1 - Prob. 11PS Ch. 3.1 - Prob. 12PS Ch. 3.1 - Prob. 13PS Ch. 3.1 - Prob. 14PS Ch. 3.1 - Prob. 15PS Ch. 3.1 - Prob. 16PS Ch. 3.1 - Prob. 17PS Ch. 3.1 - Prob. 18PS Ch. 3.1 - Prob. 19PS Ch. 3.1 - Prob. 20PS Ch. 3.1 - Prob. 21PS Ch. 3.1 - Prob. 22PS Ch. 3.1 - Prob. 23PS Ch. 3.1 - Prob. 24PS Ch. 3.1 - Prob. 25PS Ch. 3.1 - Prob. 26PS Ch. 3.1 - Prob. 27PS Ch. 3.1 - Prob. 28PS Ch. 3.1 - Prob. 29PS Ch. 3.1 - Prob. 30PS Ch. 3.1 - Prob. 31PS Ch. 3.1 - Prob. 32PS Ch. 3.2 - Prob. 1PS Ch. 3.2 - Prob. 2PS Ch. 3.2 - Prob. 3PS Ch. 3.2 - Prob. 4PS Ch. 3.2 - Prob. 5PS Ch. 3.2 - Prob. 6PS Ch. 3.2 - Prob. 7PS Ch. 3.2 - Prob. 8PS Ch. 3.2 - Prob. 9PS Ch. 3.2 - Prob. 10PS Ch. 3.2 - Prob. 11PS Ch. 3.2 - Prob. 12PS Ch. 3.2 - Prob. 13PS Ch. 3.2 - Prob. 14PS Ch. 3.2 - Prob. 15PS Ch. 3.2 - Prob. 16PS Ch. 3.2 - Prob. 17PS Ch. 3.2 - Prob. 18PS Ch. 3.2 - Prob. 19PS Ch. 3.2 - Prob. 20PS Ch. 3.2 - Prob. 21PS Ch. 3.2 - Prob. 22PS Ch. 3.2 - Prob. 23PS Ch. 3.2 - Prob. 24PS Ch. 3.2 - Prob. 25PS Ch. 3.2 - Prob. 26PS Ch. 3.2 - Prob. 27PS Ch. 3.2 - Prob. 28PS Ch. 3.2 - Prob. 29PS Ch. 3.2 - Prob. 30PS Ch. 3.2 - Prob. 31PS Ch. 3.2 - Prob. 32PS Ch. 3.2 - Prob. 33PS Ch. 3.2 - Prob. 34PS Ch. 3.2 - Prob. 35PS Ch. 3.2 - Prob. 36PS Ch. 3.2 - Prob. 37PS Ch. 3.2 - Prob. 38PS Ch. 3.2 - Prob. 39PS Ch. 3.2 - Prob. 40PS Ch. 3.2 - Prob. 41PS Ch. 3.2 - Prob. 42PS Ch. 3.2 - Prob. 43PS Ch. 3.2 - Prob. 44PS Ch. 3.2 - Prob. 45PS Ch. 3.2 - Prob. 46PS Ch. 3.2 - Prob. 47PS Ch. 3.2 - Prob. 48PS Ch. 3.2 - Prob. 49PS Ch. 3.2 - Prob. 50PS Ch. 3.2 - Prob. 51PS Ch. 3.2 - Prob. 52PS Ch. 3.2 - Prob. 53PS Ch. 3.2 - Prob. 54PS Ch. 3.2 - Prob. 55PS Ch. 3.2 - Prob. 56PS Ch. 3.2 - Prob. 57PS Ch. 3.2 - Prob. 58PS Ch. 3.2 - Prob. 59PS Ch. 3.2 - Prob. 60PS Ch. 3.3 - Prob. 1PS Ch. 3.3 - Prob. 2PS Ch. 3.3 - Prob. 3PS Ch. 3.3 - Prob. 4PS Ch. 3.3 - Prob. 5PS Ch. 3.3 - Prob. 6PS Ch. 3.3 - Prob. 7PS Ch. 3.3 - Prob. 8PS Ch. 3.3 - Prob. 9PS Ch. 3.3 - Prob. 10PS Ch. 3.3 - Prob. 11PS Ch. 3.3 - Prob. 12PS Ch. 3.3 - Prob. 13PS Ch. 3.3 - Prob. 14PS Ch. 3.3 - Prob. 15PS Ch. 3.3 - Prob. 16PS Ch. 3.3 - Prob. 17PS Ch. 3.3 - Prob. 18PS Ch. 3.3 - Prob. 19PS Ch. 3.3 - Prob. 20PS Ch. 3.3 - Prob. 21PS Ch. 3.3 - Prob. 22PS Ch. 3.3 - Prob. 23PS Ch. 3.3 - Prob. 24PS Ch. 3.3 - Prob. 25PS Ch. 3.3 - Prob. 26PS Ch. 3.3 - Prob. 27PS Ch. 3.3 - Prob. 28PS Ch. 3.3 - Prob. 29PS Ch. 3.3 - Prob. 30PS Ch. 3.3 - Prob. 31PS Ch. 3.3 - Prob. 32PS Ch. 3.3 - Prob. 33PS Ch. 3.3 - Prob. 34PS Ch. 3.3 - Prob. 35PS Ch. 3.3 - Prob. 36PS Ch. 3.3 - Prob. 37PS Ch. 3.4 - Prob. 1PS Ch. 3.4 - Prob. 2PS Ch. 3.4 - Prob. 3PS Ch. 3.4 - Prob. 4PS Ch. 3.4 - Prob. 5PS Ch. 3.4 - Prob. 6PS Ch. 3.4 - Prob. 7PS Ch. 3.4 - Prob. 8PS Ch. 3.4 - Prob. 9PS Ch. 3.4 - Prob. 10PS Ch. 3.4 - Prob. 11PS Ch. 3.4 - Prob. 12PS Ch. 3.4 - Prob. 13PS Ch. 3.4 - Prob. 14PS Ch. 3.4 - Prob. 15PS Ch. 3.4 - Prob. 16PS Ch. 3.4 - Prob. 17PS Ch. 3.4 - Prob. 18PS Ch. 3.4 - Prob. 19PS Ch. 3.4 - Prob. 20PS Ch. 3.4 - Prob. 21PS Ch. 3.4 - Prob. 22PS Ch. 3.4 - Prob. 23PS Ch. 3.4 - Prob. 24PS Ch. 3.4 - Prob. 25PS Ch. 3.4 - Prob. 26PS Ch. 3.4 - Prob. 27PS Ch. 3.4 - Prob. 28PS Ch. 3.4 - Prob. 29PS Ch. 3.4 - Prob. 30PS Ch. 3.4 - Prob. 31PS Ch. 3.4 - Prob. 32PS Ch. 3.4 - Prob. 33PS Ch. 3.4 - Prob. 34PS Ch. 3.4 - Prob. 35PS Ch. 3.4 - Prob. 36PS Ch. 3.4 - Prob. 37PS Ch. 3.4 - Prob. 38PS Ch. 3.4 - Prob. 39PS Ch. 3.4 - Prob. 40PS Ch. 3.4 - Prob. 41PS Ch. 3.4 - Prob. 42PS Ch. 3.4 - Prob. 43PS Ch. 3.4 - Prob. 44PS Ch. 3.4 - Prob. 45PS Ch. 3.4 - Prob. 46PS Ch. 3.5 - Prob. 1PS Ch. 3.5 - Prob. 2PS Ch. 3.5 - Prob. 3PS Ch. 3.5 - Prob. 4PS Ch. 3.5 - Prob. 5PS Ch. 3.5 - Prob. 6PS Ch. 3.5 - Prob. 7PS Ch. 3.5 - Prob. 8PS Ch. 3.5 - Prob. 9PS Ch. 3.5 - Prob. 10PS Ch. 3.5 - Prob. 11PS Ch. 3.5 - Prob. 12PS Ch. 3.5 - Prob. 13PS Ch. 3.5 - Prob. 14PS Ch. 3.5 - Prob. 15PS Ch. 3.5 - Prob. 16PS Ch. 3.5 - Prob. 17PS Ch. 3.5 - Prob. 18PS Ch. 3.5 - Prob. 19PS Ch. 3.5 - Prob. 20PS Ch. 3.5 - Prob. 21PS Ch. 3.5 - Prob. 22PS Ch. 3.5 - Prob. 23PS Ch. 3.5 - Prob. 24PS Ch. 3.5 - Prob. 25PS Ch. 3.5 - Prob. 26PS Ch. 3.5 - Prob. 27PS Ch. 3.5 - Prob. 28PS Ch. 3.5 - Prob. 29PS Ch. 3.5 - Prob. 30PS Ch. 3.5 - Prob. 31PS

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