Is A Full Rank Equivalent to an Overdetermined System?

[Niles]

Homework Statement

Hi

If I am dealing with an overdetermined system Ax=b, then I can (assuming A has full rank) find the unique approximative solution by least squares.

Now, in my book it says that: "For a full column rank matrix, it is frequently the case that no solution x satisfies Ax=b exactly". I assume the book is saying that A having full rank is equivalent to it being overdetermined.

Is that always the case?


Niles.

 

[Niles]

That is not always the case, I found out.