System of equations

**dwsmith** · September 25th 2011, 05:43 PM

Consider a system of linear equations $Ax=b$ . Suppose the entries of the matrices A and b are all rational numbers, and the system has a nontrivial sol. in $\mathbb{C}$ . Show that it has a nontrivial sol in $\mathbb{Q}$ .

I am not sure on how to start this.

**Deveno** · September 25th 2011, 05:59 PM

how do you find a solution to Ax = b? if you use elementary row operations only involving rational numbers, won't the results be rational?

**dwsmith** · September 25th 2011, 06:03 PM

Originally Posted by Deveno

how do you find a solution to Ax = b? if you use elementary row operations only involving rational numbers, won't the results be rational?

I don't know. I don't get it.

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