If a matrix A is 3 x 7, and we know nothing else about it, explain why its columns must be linearly dependent. (Use an explanation that does notrely solely on statements about pivots or the reduced row echelon form of A.)

Given Ais a 3×7 matrix then we have to explain why its columns are linearly dependent.

Answered: If a matrix A is 3 x 7, and we know…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If a matrix A is 3 x 7, and we know nothing else about it, explain why its columns must be linearly dependent. (Use an explanation that does not rely solely on statements about pivots or the reduced row echelon form of A.)