(Solved) : 111 Let 129698648 1 2161 1441 Find Condition Number Determinant Inverse Using Matlab B Le Q43939284 . . .
11.1 Let | 1.2969.8648 1 | .2161 .1441 (a) Find the condition number, determinant and inverse of A (using MATLAB). (b) Let B be the matrix obtained from A by rounding off to three decimal places (1.2969 H 1.297). Find the inverse of B. How do A-1 and B-1 differ? Explain how this happened. (c) Set b1 = (1.2969; 0.2161] and do x = A b1 . Repeat the process but with a vector b2 obtained from b1 by rounding off to three decimal places. Explain exactly what happened. Why was the first answer so simple? Why do the two answers differ by so much? 11.2 To see how to solve linear systems symbolically, try > B = [sin (sym (1)) sin(sym (2)); sin (sym (3)) sin(sym (4))] > c = [1; 2] > X = BIC pretty (x) AAAA Now input the matrix Cs= ( 2 1 1 symbolically as above by wrapping each number in sym. Create a numerical version via Cn = double (Cs) and define the two vectors d1 = [4; 8] and d2 = [1; 1]. Solve the systems Cs*x = d1, Cn*x = d1, Cs*x = d2, and Cn*x = d2. Explain the results. Does the symbolic or non-symbolic way give more information? 11.3 Recall the matrix A that you saved using A_equil_truss in exercise 9.1. (Enter > load A_equil_truss or click on the file A_equil_truss.mat in the folder where you saved it; this should reproduce the matrix A.) Find the condition number for this matrix. Write a well-commented script program to calculate the mean and median condition number of 1000 randomly generated 7 by 7 matrices. How does the condition number of the truss matrix compare to randomly generated matrices? Turn in your script with the answers to these questions. Show transcribed image text 11.1 Let | 1.2969.8648 1 | .2161 .1441 (a) Find the condition number, determinant and inverse of A (using MATLAB). (b) Let B be the matrix obtained from A by rounding off to three decimal places (1.2969 H 1.297). Find the inverse of B. How do A-1 and B-1 differ? Explain how this happened. (c) Set b1 = (1.2969; 0.2161] and do x = A b1 . Repeat the process but with a vector b2 obtained from b1 by rounding off to three decimal places. Explain exactly what happened. Why was the first answer so simple? Why do the two answers differ by so much? 11.2 To see how to solve linear systems symbolically, try > B = [sin (sym (1)) sin(sym (2)); sin (sym (3)) sin(sym (4))] > c = [1; 2] > X = BIC pretty (x) AAAA Now input the matrix Cs= ( 2 1 1 symbolically as above by wrapping each number in sym. Create a numerical version via Cn = double (Cs) and define the two vectors d1 = [4; 8] and d2 = [1; 1]. Solve the systems Cs*x = d1, Cn*x = d1, Cs*x = d2, and Cn*x = d2. Explain the results. Does the symbolic or non-symbolic way give more information? 11.3 Recall the matrix A that you saved using A_equil_truss in exercise 9.1. (Enter > load A_equil_truss or click on the file A_equil_truss.mat in the folder where you saved it; this should reproduce the matrix A.) Find the condition number for this matrix. Write a well-commented script program to calculate the mean and median condition number of 1000 randomly generated 7 by 7 matrices. How does the condition number of the truss matrix compare to randomly generated matrices? Turn in your script with the answers to these questions.
Expert Answer
Answer to 11.1 Let | 1.2969.8648 1 | .2161 .1441 (a) Find the condition number, determinant and inverse of A (using MATLAB). (b) L…
OR