Let A be a nonsingular n n matrix, and suppose that A = L1D1U1 = L2D2U2, where L1 and L2
Chapter 6, Problem 7(choose chapter or problem)
Let A be a nonsingular n n matrix, and suppose that A = L1D1U1 = L2D2U2, where L1 and L2 are lower triangular, D1 and D2 are diagonal, U1 and U2 are upper triangular, and L1, L2, U1, U2 all have 1s along the diagonal. Show that L1 = L2, D1 = D2, and U1 = U2. [Hint: L1 2 is lower triangular and U1 1 is upper triangular. Compare both sides of the equation D1 2 L1 2 L1D1 = U2U1 1 .]
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