- #1

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## Homework Statement

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.

## Homework Equations

## 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.