Why Isn't the Least Square Solution Unique with Linearly Dependent Columns?

[td21]

Homework Statement

If a matrix A has linearly dependent columns and b is a vector, then the least square solution is not unique.

Homework Equations

The Attempt at a Solution

I know that the "projection" onto column space of A is unique, but why the least square solution isn't?

 

[td21]

help?

 

[MaxManus]

If you have linearly dependent columns, you have too few independent equations to get a unique? Its like trying to describe only one point with a line.
Or am I wrong? It's two years since I had the course

 

[MaxManus]

http://en.wikipedia.org/wiki/Linear_least_squares_(mathematics )

B = (X'X)^-1 X'y

(X'X)^-1 doesn't it have to have linearly independent columns if you want to calculate the inverse?

Again I'm only guessing