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Sparky

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General linear algebra question

If every column of an augmented matrix contains a pivot, then is the corresponding system always consistent?  Why or why not?

Thanks in advance to anyone who answers!

Sylvia104

Banned

Registered: 2011-09-19

Posts: 29

Re: General linear algebra question

In the case of an

augmented matrix:

(1) if

then the system will not always be consistent (if consistent it will have infinitely many solutions),

(2) if

then it will be consistent (and its solution is unique),

(3) if

then it will also be consistent (but will have infinitely many solutions).

Last edited by Sylvia104 (2011-09-19 07:58:12)