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

Ax ≤ b, assuming A is nxn and solution exists

2. Relevant equations

3. The attempt at a solution

I don't know of any concrete methods offhand. A grad student suggested rearranging it to:

Ax - b ≤ 0, zero vector

Then I don't know where to go from here. I was thinking of multiplying by [itex]x^{T}[/itex] to get [itex]x^{T}Ax - x^{T}b ≤ 0[/itex] , 0 a scalar now. Is this a valid method? If not, I wouldn't mind any direction to theorems that say otherwise. Then I was thinking of solving for the null space of A and finding some other method to make [itex]x^{T}b[/itex] ≥ 0 (would also like some literature or reference to methods involving this operation).

aye or nay, if nay, can someone suggest the general accepted methods and perhaps the name of what this kind of problem is. Thanks in advance.

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# Homework Help: Matrix inequality

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