Find the determinant and inverse of a matrix whose entries are all '1s' ( ones ) except for the diagonals which are '0s' ( zeros )
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(1) Let A = (see attachment), the nxn matrix with all entries equal to 1 expect diagonal entries, which are equal to 0. Find the determinant .
(2) For the above matrix A, find the inverse.
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Solution Summary
The determinant and inverse of a matrix whose entries are all '1s' ( ones ) except for the diagonals which are '0s' ( zeros ) are found. The solution is detailed.
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See the attached file.
Expanding the matrix determinant by minors , I obtain for the nxn matrix D = (-1)^(n+1) x (n-1).
Try n =3 D =2 ...
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