(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the following are equivalent:

1. N(A)=0

2. A is nonsingular

3. Ax=b has a unique solution for each b that exists in R^n.

2. Relevant equations

3. The attempt at a solution

I think you prove this by showing that 1 implies 2, 2 implies 3, & 3 implies 1.

But after that I don't know how to prove that.

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# Homework Help: Linear Algebra Vector Spaces: Prove equivalence

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