Analytical Solution for Lower Triangular Matrix w/ Non-Zero Nth Column

[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/wikipedia/en/math/5/4/a/54a4f76e238ad68e6cf4b0f7c84e949b.png