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10.001 FALL 2002HOMEWORK ASSIGNMENT #9ASSIGNED TUESDAY NOVEMBER 19DUE TUESDAY NOVEMBER 26, 12:00 NOONPlease make sure the files contain the appropriate comment lines.PROBLEM 9.1Write the code for the low_tri function, which:i) Returns matrix M, which turns the coefficient matrix A into an uppertriangular matrix U: MA=U. Matrix A will be passed to the function when thefunction is called. Please refer to Problem 9.3ii) Make sure the code checks for zero entries in A and entries smaller than thetolerance limit tollim and gives the error message if necessary. tollim willbe passed to the function when the function is called. Please refer to Problem9.3.iii) Returns the position of the aij that is smaller than tollimiv) Does not us the standard Matlab function lu.PROBLEM 9.2Write the code for the back_sub function, which:i) performs the backsubstitution procedure, given the upper triangular matrix Uand the load vector bii) returns the solution vector xPROBLEM 9.3Write a script file, which solves the following systems of linear equations using thefunctions you have just created, let tollim=0.001.If an error message appears for System of Linear Equations 1 (SLE1) or SLE2 (seebelow) (one of aij is below the tolerance limit), find the way to make the system solvablegiven the information about which entry of A is too small assuming that this is the onlyproblem you have. Please describe your way in the script file as comments. Then changethe SLE1 and SLE2 into solvable forms if necessary and solve them.Turn in your script file, function files low_tri.m and back_sub and solutions of thetwo SLEs.SLE 1: A = 1 5 3 2- 4 2 1- 3 2 1- 3 2 2- 3 2 1-, b = −0321SLE 2: A = −−−423011123, b


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MIT 10 001 - HOMEWORK ASSIGNMENT #9

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