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Homework Statement
In the least squares method the vector x* that is the best approximation to b statisfies the Least squares equation:
[tex]A^T A x^*= A^T b [/tex]
Prove that there's always a solution to this equation.
Homework Equations

The Attempt at a Solution
I distinct 2 situations [tex]A^T A [/tex] is invertible and it isn't invertible. If it's invertible then there's no problem [tex]x^*= (A^T A)^{1} A^T b [/tex]
But how I prove that it works in the noninvertible case?