I was wondering if its possible to know if a matrix is invertible without row reducing it in attempt to make it I. If the matrix is not nxn, it is never invertible?

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- Oct 3rd 2011, 04:25 PMKumainvertible matrix
I was wondering if its possible to know if a matrix is invertible without row reducing it in attempt to make it I. If the matrix is not nxn, it is never invertible?

- Oct 3rd 2011, 04:28 PMDrexel28Re: invertible matrix
- Oct 3rd 2011, 04:34 PMKumaRe: invertible matrix
- Oct 3rd 2011, 07:19 PMDrexel28Re: invertible matrix
Well, since you liked the last explanation, perhaps one in the same vein. Pretend for a second that a matrix really is just a linear transformation , then one only has to check any of the following equivalent conditions:

1) is injective

2) is surjective

3) does not have zero as an eigenvalue

4)

And there are many more, some of which are very similar to the ones I listed (e.g. 1) is easily seen to be eqiuvalent to the existence of a left inverse). - Oct 3rd 2011, 08:57 PMFernandoRevillaRe: invertible matrix