detrminant of a lower triangular matrix with an exception (Nth column is non-zero)

fourier1980

Hi folks,

is there an analytical solution for the determinant of the following matrix:

- -
| A B |
| C d |
- -

where A is a n-1 x n-1 lower triangular matrix and B and C are n-1x1 and 1xn-1 matrices and d is a non-zero number.

algebrat

Do your blocks satisfy anything so that you can use a trick from:

http://en.wikipedia.org/wiki/Determinant#Block_matrices

Are A or d invertible? (The product BC is an nxn matrix.)

If A is invertible, then you have:

http://upload.wikimedia.org/wikipedi...f7c84e949b.png

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fourier1980	detrminant of a lower triangular matrix with an exception (Nth column is non-zero) Tweet Hi folks, is there an analytical solution for the determinant of the following matrix: - - \| A B \| \| C d \| - - where A is a n-1 x n-1 lower triangular matrix and B and C are n-1x1 and 1xn-1 matrices and d is a non-zero number.

algebrat	Do your blocks satisfy anything so that you can use a trick from: http://en.wikipedia.org/wiki/Determinant#Block_matrices Are A or d invertible? (The product BC is an nxn matrix.) If A is invertible, then you have: http://upload.wikimedia.org/wikipedi...f7c84e949b.png Attached Thumbnails