# Linear algebra unique solutions

charlies1902
This is just a general question.

When a coefficient matrix for a linear system has a determinant equal to 0. That means the coefficient matrix does not have an inverse, thus the system does not have a unique solution.

Is the above statement correct?

What exact is a unique solution? Is it basically just one without free variables?

## Answers and Replies

Science Advisor
Homework Helper
That's essentially correct. Might be best though if you thought about why it's true so you can answer this yourself. If M is your coefficient matrix, then det(M)=0 means Mx=0 has a solution. So Mx=0 has an infinite number of solutions. And the solution not being unique could mean either you have an infinite number of solutions (i.e. free parameters) or you might have no solutions. Can you give an example?