Which of the following statements are true? (Proposition 2.50 included) Proposition 2.50: matrix representation of iterative schemesLet A € Rdxd, and let D, L,U € Rdxd be diagonal, strictly lower triangularand strictly upper triangular matrices withA = D-L-U.Then Jacobi's method can be written in the formz(k+1) = D−¹(b + (L+U)x(k)) Vk €N,and the Gauss-Seidel method can be written in the form(D − L)x(k+¹) = b + Urk) Vk € N.(2.14)(2.15)(2.16) a. When A is upper triangular, then Jacobi's method and the Gauss-Seidel method areidentical.b.Consider the splitting A = D-L-U as in Proposition 2.50. If A is symmetric, then L=U.☐ c. When A is lower triangular, then the Gauss-Seidel method finds the exact solution xof the system Ax=b in one single step.d. When ||Allo>1, then Jacobi's method is guaranteed not to converge.

Hint: Here we need to discuss about the Gauss-Seidel method and Jacobi method.

a. When A is upper triangular, then Jacobi's method and the Gauss-Seidel method are identical. b. Consider the splitting A =D - L - U as in Proposition 2.50. If A is symmetric, then L=U. C. When A is lower triangular, then the Gauss-Seidel method finds the exact solution x of the system Ax=b in one single step. Od. When ||A||>1, then Jacobi's method is guaranteed not to converge.