Linear algebra

Given 3 simultaneous equations with 3 unknowns each, how do i determine if they have 0, 1, or infinite sets of solutions? I know how to convert the equations into reduced echelon form, if it helps. Thanks.

>>10
That "then let N go to 9" joke isn't entirely unfounded in reality, you know. People with a Ph.D in mathematics often have had their head so well and truly fucked that they won't even feel N-dimensional problems and their limp little dicks.
Anyway, who knows whether they're thinking of linear algebra geometrically or just reducing geometrics to linear algebra. I'm not a mathematician myself, I just know enough of them to appreciate the mathematician jokes.