Hi there,
If a system is "inconsistent" there are no solutions to it.
If you use Gaussian elimination and you are left with a matrix like:
1 0 3
0 0 7
Then it's inconsistent. You can tell that, because the second row implies that 0 = 7, which is obviously false. Basically, you are looking for rows that imply something false.
Let me know if you have any questions,
Scott
MIT Graduate
College degree in math... proficient in all levels -- from algebra to calculus