Suppose we have a nonhomogeneous system of 5 equations in 7

Suppose we have a non-homogeneous system of 5 equations in 7 unkowns.

1. can the system have no solution? Why?

2. Can the system have infinity many solutions? Why?

3. Can the system have a unique solution? Why?

Given that a non-homogeneous system of 5 equations in 7 unkowns.

This system have infinity many solutions.

Because, 7 unknowns can\'t find out from 5 equations.

From 5 equations we can know only 5 unknowns. Remaining 2 unknowns can be taken as variables.

Variables may have any number.

As variables has different values, the system has infinitely many solutions.

Therefore, a non-homogeneous system of 5 equations in 7 unkowns has infinitely many solutions.