# using Matlab or Octave to solve the matrix?

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Math 471/571 Fall 2016 Homework: Due Friday, 11/4. 101 100 200 −99 2 5 102 101 197 −97 −1 9 For 𝐴 = ( ) and 𝑏⃗ = ( ), the exact solution to 𝐴𝑥 = 𝑏⃗ is 𝑥 = ( ). 303 300 602 −297 1 17 −202 −200 −400 199 3 −7 Use Matlab (or something similar) for this problem. Set the display to format long . a) Find Κ ∞ (𝐴). b) According to the heuristic given in class, how many digits of accuracy would you expect in a computed solution to 𝐴𝑥 = 𝑏⃗? (Matlab uses double precision arithmetic, which is about 16 digit arithmetic). c) Using the built-in solve routine, find an approximate solution 𝑥̃ for 𝐴𝑥 = 𝑏⃗. d) Calculate the relative error (using the infinity norm) for the approximate solution from part (c). e) How many significant digits did you get in the approximate solution?

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