Is there an example of an inconsistent linear system with more variables than equations?

Question

I believe that is impossible because there would always be free variables. Does anyone know if that is correct?

Answer 1

This concept is linear algebra.

The expressions that contain the variables can be translated into vectors. If the vectors span a space of dimension less than the number of equations you can indeed have no solutions. Otherwise there is a solution.

Answer 2

No, it is not correct. Take, for instance, the system$$\left\{\begin{array}{l}x+y+z=0\\x+y+z=1.\end{array}\right.$$