Problem 1. Solve the linear system Ax = f. where A is defined as an arrow...

 

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Problem 1. Solve the linear system Ax = f. where A is defined as an arrow matrix. x is the solution vector, and f is the right-hand side vector of given data. To be more precise, do the following: a) Derive a modified Thomas algorithm that solves the linear system Ax = f of order 4, where A is defined as the following arrow matrix: A = [b 0 0 bz 0 0 U = 0 by C3 az a3 ba a In the first step of the algorithm, generate the upper triangular matrix [B0 0 C1 0 2 0 0 0 B3 3 084 0 0 0 CI i.c. determine ; for all i e{1,2,3,4), and the modified right-hand side vector g. In the second step, use back substitution to solve the linear system Ux=g for the solution .x. b) Generalize the modified Thomas algorithm derived in Part a) to solve the linear system Ax = f of order n. c) Use the result found in Part b) to write a MATLAB script that is able to solve the linear system Ax = f of ordern with user-defined arrow matrix A and user-defined right-hand side vector f. Furthermore, store the matrix A in a memory-efficient way by storing only the vectors a, b, and e associated with the a-, by-, and c-values, respectively. Apply this MATLAB script to the case in which 3000 0 7 0-200 0 6 0 0 40 0 -5 0 0 01 0 5 0 0 00-8 4 5 3 82 9 -2 440 and Problem 1. Solve the linear system Ax = f. where A is defined as an arrow matrix. x is the solution vector, and f is the right-hand side vector of given data. To be more precise, do the following: a) Derive a modified Thomas algorithm that solves the linear system Ax = f of order 4, where A is defined as the following arrow matrix: A = [b 0 0 bz 0 0 U = 0 by C3 az a3 ba a In the first step of the algorithm, generate the upper triangular matrix [B0 0 C1 0 2 0 0 0 B3 3 084 0 0 0 CI i.c. determine ; for all i e{1,2,3,4), and the modified right-hand side vector g. In the second step, use back substitution to solve the linear system Ux=g for the solution .x. b) Generalize the modified Thomas algorithm derived in Part a) to solve the linear system Ax = f of order n. c) Use the result found in Part b) to write a MATLAB script that is able to solve the linear system Ax = f of ordern with user-defined arrow matrix A and user-defined right-hand side vector f. Furthermore, store the matrix A in a memory-efficient way by storing only the vectors a, b, and e associated with the a-, by-, and c-values, respectively. Apply this MATLAB script to the case in which 3000 0 7 0-200 0 6 0 0 40 0 -5 0 0 01 0 5 0 0 00-8 4 5 3 82 9 -2 440 and