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any help or light on this question would be hugely appreciated!!

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- Nov 11th 2012, 01:14 PMkaya2345help needed!!! proof of invertible matrices
The question has been attached as an image.

any help or light on this question would be hugely appreciated!!

thank you http://static1.tsrfiles.co.uk/4.7/im...lies/smile.png - Nov 11th 2012, 01:29 PMPlatoRe: help needed!!! proof of invertible matrices
- Nov 11th 2012, 01:32 PMkaya2345Re: help needed!!! proof of invertible matrices
- Nov 11th 2012, 01:57 PMHallsofIvyRe: help needed!!! proof of invertible matrices
That shows, I think, that the

**minimum**number of 1s in such an invertible n by n matrix is n. But the question was about the**maximum**number. We do know that if a matrix has two columns the same, it is not invertible. I think we can avoid that by having a 0, at a different row, in each column. That implies that the maximum number of 1s in such an invertible n by n matrix is $\displaystyle n^2- n$. - Nov 11th 2012, 02:02 PMkaya2345Re: help needed!!! proof of invertible matrices
- Nov 11th 2012, 02:21 PMPlatoRe: help needed!!! proof of invertible matrices