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Consider the following system of linear equation:
2x1 - 6x2 - x3 = -38-3x1 -x2 + 7x3 = -34-8x1 + x2 - 2x3 = -20
a) Check whether system has no solution, infinite number of solutions or ill-conditions. Perform this checking from the coefficient and constant matrices. b) Manually solve the system of linear equation using Gauss elimination method with partial pivoting. Consider 3 decimal places. Show all steps of your computation in detail. c) Once you obtain the solution, go to MATLAB's command window to compute the solutions by using Cramer's Rule and verify the correctness of the solution. d) Considering the values obtained from MATLAB as true value, compute the absolute relative errors for the values that you manually calculated for each of variables.e) Include all your computation details, and MATLAB command window activities in your file to be submitted..
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