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I have a confusion regarding solving an overdetermined system of equations. Consider M equations and N unknowns. If M > N, then the system is overdetermined. Now since when expressed in matrix form, the column rank is N (in other words N degrees of freedom), the N equations must be linear dependent and reducible to a set of equations <= M. So there would be a unique solution. Then why would a solution not exist for an overdetermined system. I can see from geometry that for in two dimensions, a solution might not exist for parallel lines or three lines, but can't see it from a formal point of view because of linear dependence between them.

A follow up question would be what would take to solve an overdetermined system?

Relevant links:

http://en.wikipedia.org/wiki/Overdetermined_system

If someone could please explain, it would be very helpful.

thank you,

Sam

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# Overdetermined system

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