If the n n matrix A can be expressed as A = LU, where L is a lower triangular matrix and
Chapter 1, Problem 40(choose chapter or problem)
If the n n matrix A can be expressed as A = LU, where L is a lower triangular matrix and U is an upper triangular matrix, then the linear system Ax = b can be expressed as LUx = b and can be solved in two steps: Step 1. Let Ux = y, so that LUx = b can be expressed as Ly = b. Solve this system. Step 2. Solve the system Ux = y for x. In each part, use this two-step method to solve the given system. (a) 100 230 241 2 1 3 012 004 x1 x2 x3 = 1 2 0 (b) 200 410 3 2 3 3 5 2 041 002 x1 x2 x3 = 4 5 2
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