Is the trivial solution a unique solution?

[darthxepher]

If the only solution to Ax = b is the trivial solution, then is that solution considered unique?

 

[Office_Shredder]

If b is non-zero, there is no trivial solution.

If b is zero, and A is invertible, then yes, x=0 is the unique solution

 

[darthxepher]

Do you know how to tell if the least squares approximation exists?

 

[adriank]

If the only solution to Ax = b is the trivial solution, then is that solution considered unique?

If it's the only solution, then by definition it's unique.

 

[HallsofIvy]

It doesn't matter whether it is trivial or not, "only solution"= "unique solution".

I have no idea what "Do you know how to tell if the least squares approximation exists?" has to do with "unique solutions" but approximations, whether good or bad, always exist.