For example, in linear algebra if the number of constraints ( independent equations ) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist.
32.
For if there are at least as many independent equations as unknowns that will eliminate any stretches of overlap of the equations'surfaces in the geometric space of the unknowns ( aside from possibly a single point ); and if the rank of the augmented matrix exceeds ( necessarily by one if at all ) the rank of the coefficient matrix then the equations jointly contradict each other.
