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How do I formally prove that elementary row operations do not change the set of solutions to a system of linear equations?

Thanks.

- Thread starter adartsesirhc
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- #1

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How do I formally prove that elementary row operations do not change the set of solutions to a system of linear equations?

Thanks.

- #2

quasar987

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Then elementary row operations are the same as either permuting two equations (obviously doesn't change the solutions!), multiplying one equations by a constant (doesn't change the solutions as you can probably easily see), and multipling an equation by a constant and adding the resulting equation to another. If you think about it for a second, you'll see why this doesn't change the solutions either.

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