Can I assume that an equation (with 3 variables) is unsolvable if its determinant equals zero.Sure, it not true if all it's other determinants are zero as well, but it seems to be unlikely
it is true for a determinant such as (1,0,0),(0,1,0),(0,0,1) but thats not a real equation.
if this is the case is there an easy way to prof that? otherwise could anyone provide an example with for which this rule doesn't work.