# Conditions on overdetermined linear system to be consistent?

1. Apr 15, 2012

### mosawi

1. The problem statement, all variables and given/known data

2. Relevant equations

An overtdetermined system - If m > n, then the linear system Ax = b is inconsistent for at least one vector b in ℝ^n.

3. The attempt at a solution

If m > n (more rows than columns), in which case the column vectors of A cannot span ℝ^m￼ (fewer vectors than the dimension of ℝ^m).

So, there is at least one vector b in ℝ^m that is not in the column space of A, and for that b the system A x = b is inconsistent by Theorem 4.7.1 which states A system of linear equations ￼ is consistent if and only if b is in the column space of A.

[STRIKE]So the conditions that must be imposed on b must be to zero out variables? I know this is wrong but I don't really know what to do?[/STRIKE]

******************UPDATE******************

I think I solved it guys, can someone check my solution and tell if its correct if not, what do I need to do to make it correct. I've attached the solution to this poste. Thanks.

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Last edited: Apr 16, 2012