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(15/100 pts) We want to check the convergence criteria of two stationary iterative methods, Jacobi and Gauss-Seidel methods, to solve Ax = b. If we split matrix A such that A = D + L + U and define an iteration matrix T that satisfies z = Tx + c. A matrix D is a diagonal matrix, and L and U are strictly lower and upper triangular matrix, respectively We'd like to derive T matrix as a function of D, L, U, and/or their inverse matrices: TJAC for the Jacobi method and Tcs for the Gauss-Seidel method. (a) (5 pts) What are the expressions for the TJAc and Tos? (b) (10 pts) Consider the following 4 x 4 matrix system. Compute the TJAc and Tos and calculate the spectral radius of each matrix. (Hint: Use the "eig(B)" command in Matlab to compute the eigenvalues of a matrix B). Based on the value of the spectral radius, will the Jacobi and Gauss-Seidel iteration methods will work to solve this system? 1 49 16 4 9 16 25 9 16 25 36 16 25 36 49 30 54 86 126 T3 (15/100 pts) We want to check the convergence criteria of two stationary iterative methods, Jacobi and Gauss-Seidel methods, to solve Ax = b. If we split matrix A such that A = D + L + U and define an iteration matrix T that satisfies z = Tx + c. A matrix D is a diagonal matrix, and L and U are strictly lower and upper triangular matrix, respectively We'd like to derive T matrix as a function of D, L, U, and/or their inverse matrices: TJAC for the Jacobi method and Tcs for the Gauss-Seidel method. (a) (5 pts) What are the expressions for the TJAc and Tos? (b) (10 pts) Consider the following 4 x 4 matrix system. Compute the TJAc and Tos and calculate the spectral radius of each matrix. (Hint: Use the "eig(B)" command in Matlab to compute the eigenvalues of a matrix B). Based on the value of the spectral radius, will the Jacobi and Gauss-Seidel iteration methods will work to solve this system? 1 49 16 4 9 16 25 9 16 25 36 16 25 36 49 30 54 86 126 T3