Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 24: 59

It is possible for a system of linear equations with fewer equations than variables to have no solution, for example $$x+y+z=1, \quad x+y+z=0.$$ It is easy to see that the above system has no solutions.

It is possible for a system of linear equations with fewer equations than variables to have no solution, for example $$x+y+z=1, \quad x+y+z=0.$$ It is easy to see that the above system has no solutions.