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Math and science::Algebra
Determinant from pivots
Let \( A \) be a matrix that is decomposed through elimination to \( A = LU
\). The truth of the following statements allow us to read the determinant of
\( A \) from the pivots that are placed along the diagonal of \( U \):
- If \( B = CD \) then \( \text{det}(B) = \text{det}(C) \text{det}(D) \; \).
- [what statement?]
- All entries along the diagonal of \( L \) are 1.
From these statements, we can see that the determinant of \( A \) is the product of the pivots that are placed along the diagonal of \( U \).
