1. Upper-Triangular Linear Systems

Theorem 1.1 (Back Substitution). Suppose that AX = B is an upper-triangular system. If

ak,k = 0 for k = 1, 2, . . . , N, (1.1)

then there exists a unique solution to system:

for k = N - 1, N - 2, . . . , 1. (1.2)

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