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If I have a system of N linear equations with N unknowns, how do I know if each unknown has atleast one solution. I havn't taken any formal classes in linear algebra, so please if you use any abstract terminology associated with linear algebra, explain it please. I would appreciate any help.

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    you're absolutely right2012-11-27

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  • Take a look at this link explaining where a certain matrix is proven to be non invertivible using a system of linear equations.
  • Also read this Wikipedia article explaining the properties of a system of linear equations.