Question

A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique​ solution? Explain.

Answer 1

So such system with fewer equations than unknowns can never have a unique solution.

Explanation:

Linear equations are equations which contain variable with degree 1.

The variables can be 1 or 2 or any other number

say there are n varaibles

Then to solve this we must have n independent equations.

If number of equations are less than number of variables we can have parametric solutions only with infinite points lying on it.

There is no chance for this to have a unique solution.

For unique solutions, there must be equal number of equations with the variables and the determinant formed by the coefficients should not be 0.

So such system with fewer equations than unknowns can never have a unique solution.