What is the problem with over-determined systems in linear algebra? Do they always have no solution? Is there a proof of that?

erwachsenc6 2022-10-13 Answered
What is the problem with over-determined systems in linear algebra? Do they always have no solution? Is there a proof of that?
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Answers (1)

Steinherrjm
Answered 2022-10-14 Author has 12 answers

An overdetermined system (more equations than unknowns) is not necessarily a system with no solution. If one or more of the equations in the system (or one or more rows of its corresponding coefficient matrix) is/are (a) linear combination of the other equations, so the such a system might or might not be inconsistent.
And some systems which are not overdetermined (number of equations = number of unknowns) have no solutions.
What is true is that whenever we have an inconsistent system of equations, there is no solution.
My point is that you understand that a system of linear equations has no solution if and only if it is inconsistent.
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