Critical values and linear least squares

[sam.pat]

I have a question about Linear least squares:

In Linear least squares, For any critical point "x" it must follow the linear system:
A(Transpose) * Ax = b * A(Transpose) where x is the critical point.

But here x is an n vector, so does that mean there are as many critical points (x) as there are columns?

So in case of an quadratic polynomial : 1 + X2*t + X3*t^2 with three parameters, would we have three critical points?

|1 t1 t1^2 |
|1 t2 t2^2 |
|1 t3 t3^3 |
|1 ... ... |
|1 ... ... |

Thanks in advance

 

[lippyka]

No, the number of critical points is determined by the number of variables in the system, not the number of columns in the matrix. In the example you gave, there would only be one critical point since there are only three variables.