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

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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.
 
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