If the only solution to Ax = b is the trivial solution, then is that solution considered unique?
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
Do you know how to tell if the least squares approximation exists?
If it's the only solution, then by definition it's unique.
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.
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