The 'Least Squares' solution to Ax=bAx=bAx=b is found by solving:
ATAx=ATbA^T A x = A^T bATAx=ATb
Ax=bA x = bAx=b
AATx=bA A^T x = bAATx=b
det(A)x=b\det(A)x = bdet(A)x=b