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gibson:teaching:fall-2014:math445:solveafb

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 — gibson:teaching:fall-2014:math445:solveafb [2014/09/12 10:42] (current)gibson created 2014/09/12 10:42 gibson created 2014/09/12 10:42 gibson created Line 1: Line 1: + + % A script file to solve the following 5 x 5 system ​ + % + % + %       c f1 + f2  =  0 + %  f2 - 2 f3 + f4  =  5 + %       f1 + c f3  =  4 + %     3 f1 + 7 f5  = -1 + %       f2 - c f4  =  2 + % + % where c = sqrt(2); + % + % Rewrite this as an Ax=b problem, or Af=b. + % + % c  1  0  0  0    f1      0 + % 0  1 -2  1  0    f2      5 + % 1  0  c  0  0    f3  =   4 + % 3  0  0  0  7    f4     -1 + % 0  1  0 -c  0    f5      2 + + % Here's a slick way to enter the above matrix + + c = sqrt(2); + A = zeros(5,5); + + A(1, [1 2]) = [ c 1 ]; + A(2, [2 3 4]) = [ 1 -2 1 ]; + A(3, [1 3]) = [ 1 c ]; + A(4, [1 5]) = [ 3 7 ]; + A(5, [2 4]) = [ 1 -c ]; + + b = [0 5 4 -1 2]'; + + f = A\b; + 