Consider linear iterations to solve linear systems with the following coefficient matrices 1 0 1 1...

 

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Consider linear iterations to solve linear systems with the following coefficient matrices 1 0 1 1 0.5 0.5] (i) A=-1 1 0 (ii) A = 0.5 1 0.5 3 1 -2 3 0.5 0.5 1 a) (3 points) Verify that for the matrix in (i), the Jacobi iteration is convergent for all initial guesses, but GS is not, and state the reason for the convergence or no convergence. b) (3 points) Verify that for the matrix in (ii), the GS iteration is convergent for all initial guesses but Jacobi is not, and state the reason for the convergence or no convergence. c) (1 point) Verify that among 2 x 2 matrices, there is no example like the above. That is, either both Jacobi and GS iterations converge for any x, or they both do not converge. Consider linear iterations to solve linear systems with the following coefficient matrices 1 0 1 1 0.5 0.5] (i) A=-1 1 0 (ii) A = 0.5 1 0.5 3 1 -2 3 0.5 0.5 1 a) (3 points) Verify that for the matrix in (i), the Jacobi iteration is convergent for all initial guesses, but GS is not, and state the reason for the convergence or no convergence. b) (3 points) Verify that for the matrix in (ii), the GS iteration is convergent for all initial guesses but Jacobi is not, and state the reason for the convergence or no convergence. c) (1 point) Verify that among 2 x 2 matrices, there is no example like the above. That is, either both Jacobi and GS iterations converge for any x, or they both do not converge.