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This program solves Ax=b, using Gaussian elimination with partial pivoting and back substitution. *A should be a nxn matrix, and b should be a nx1 vector. These matrices should have been written in text documents named "A.txt" and "b.txt", respectively. They should have the same number of lines. Each line represents a row. Example:For "A.txt" 3.14 1.59 2.65 3.58 9.79 3.23 8.46 2.64 3.38 3.27 9.50 2.88 4.19 7.16 9.39 9.37 For “b.txt” 5.10 5.82 0.97 4.94 *They should also be in the same folder with the program. *The solution file will be written to a file named "x.txt" in that file. *If A is singular or nearly singular (any number which its absolute value is smaller than 1e-6 will be converted to 0), a warning will appear in the console and no x file will be generated. *If the matrix A is 2x2, the condition numbers will be shown in the console. *****The Case of High Condition Numbers***** A=[1.000 1.000 1.000 1.001] b1=[2.000 2.000]T b2=[2.000 2.001]T The condition number, using infinity norm, of the matrix A is 4003.81 The condition number, using one norm, of the matrix A is 4003.81 x1=[2 0]T x2=[1.00012 0.999881]T Since the condition number is too high (>>1), the solution is very sensitive to the small changes as we can see from the example above.
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Gaussian elimination with partial pivoting and back substitution
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