Say we have a set of linear equations given by a~x =~y. if a is invertible, we know that the solution for ~x is ~x = a −1~y. however, what if a is not a square matrix? in 16a, you saw how this problem could be approached for tall "standing up" matrices a where it really wasn’t possible to find a solution that exactly matches all the measurements, using linear least-squares. the linear least-squares solution gives us a reasonable answer that asks for the "best" match in terms of reducing the norm of the error vector.