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Answer: [M] When the right side of an equation Ax = b is
Chapter , Problem 19E(choose chapter or problem)
[M] When the right side of an equation Ax = b is changed slightly—say, to When A is invertible, the condition number of A, written as cond(A), produces a bound on how large the relative change in x can be: In Exercises 17–20, solve , and show that the inequality (2) holds in each case. (See the discussion of ill-conditioned matrices in Exercises 41–43 in Section 2.3.)
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QUESTION:
[M] When the right side of an equation Ax = b is changed slightly—say, to When A is invertible, the condition number of A, written as cond(A), produces a bound on how large the relative change in x can be: In Exercises 17–20, solve , and show that the inequality (2) holds in each case. (See the discussion of ill-conditioned matrices in Exercises 41–43 in Section 2.3.)
ANSWER:Solution 19EStep 1 of 4Write the matrices, Use the following Matlab commands to solve Enter the matrices:>> A=[7 -6 -4 1; -5 1 0 -2; 10 11 7 -3; 19 9 7 1]A =7 -6 -4 1-5 1 0 -210 11 7 -319 9 7 1>> b=[0.1; 2.888; -1.404; 1.462]b =0.10002.8880-1.40401.4620>> deltab=10^(-4)*[0.49;-1.28;5.78;8.04]deltab =1.0e-03 *0.0490-0.12800.57800.8040