Show that the determinant of an upper or lower triangular
Chapter 8, Problem 8.5(choose chapter or problem)
Show that the determinant of an upper or lower triangular matrix is the product of its main diagonal elements. Hint: Every term but one of the sum (8.1) contains a factor ai j with i > j and a term ai j with i < j, and one of these terms must be zero if the matrix is upper or lower triangular. The exceptional term corresponds to the permutation p that leaves every number 1, 2, , n unmoved.
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