HW4_solution - U Back-substitution gives x = 1-3 1 1 2.5.21...

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EE441 HW#4 Solution Spring 2007 Instructor : Dr. Jonckheere TA: Ben Raskob Due Date 2/8/2007 Review Exercise 1.13 We are given two linear systems of equations, Lc = b and Ux = c . Solving Lc = b is made simple because L has zeros above the diagonal: 1 0 0 4 1 0 1 0 1 c 1 c 2 c 3 0 0 1 The first row gives us c 1 = 0. The second row gives 4 c 1 + c 2 = 0, yielding c 2 = 0. Row three has c 1 + c 3 = 1, yielding c 3 = 1. Therefore, c = 0 0 1 Solving Ux = c is also made simple from the upper-triangular form of
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Unformatted text preview: U . Back-substitution gives x = 1-3 1 1 2.5.21 The graph on the top-right of p.123 has 4 nodes, so M is a 4x4 matrix. M = 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 M 2 = 3 2 2 2 2 3 2 2 2 2 3 2 2 2 2 3 ( M 2 ) ij = a i 1 a 1 j + ... + a in a nj and we get a ik a kj = 1 when there is a 2-step path i to k to j . 2...
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