Let A be an mn matrix of rank r. If ghe linear system Ax=b has a solution

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Let A be an m×n matrix of rank r. If ghe linear system Ax=b has a solution for each b£R^m, then

1) m=r

2) the column space of A is proper subspace of R^m.

3) the null space of A is a non-trivial subspace of Rⁿ whenever m=n.

4) if m>=n implies m=n.

Related Book For answer-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

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Posted Date: Jan 24, 2023 02:15 AM

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Let A be an mn matrix of rank r. If ghe linear system Ax=b has a solution

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Elementary Linear Algebra with Applications

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