2. If A is an n x n matrix, show that det A = 0 if and only if some column of A is a linear combination of the other columns.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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If A is an n×n matrix, show that detA=0 if and only if some column of A is a linear combination of the other columns.

2. If A is an n × ʼn matrix, show that det A = 0 if and only if some column of A is a linear combination of the other columns.
Transcribed Image Text:2. If A is an n × ʼn matrix, show that det A = 0 if and only if some column of A is a linear combination of the other columns.
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