Determining Whether a System of Linear Equations Is Inconsistent
Determining Whether a System of Linear Equations Is Inconsistent 1- Is getting a false equation during the normal process of solving a system of linear equations (e.g. substitution/elimination) is the only way we ensure this system has no solutions? 2- If no, what other ways available?
Would you count gaussian (aka row) elimination as a possibility? Then there's no solution iff you get a row of zeros except a nonzero at the far right in the augmented matrix that you're doing row elimination on.