Consider the system Ağ = b given by X 1 2 -1 4 -1 X2 1 4 -1 0 -1 0 0 0 -1 4 0 0 -1 13 -1 0 0 4. -1 0 0 -1 0 -1 4. 0 0 -1

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Consider The System Ag B Given By X 1 2 1 4 1 X2 1 4 1 0 1 0 0 0 1 4 0 0 1 13 1 0 0 4 1 0 0 1 0 1 4 0 0 1 1 (125.18 KiB) Viewed 89 times

Consider the system Ağ = b given by X 1 2 -1 4 -1 X2 1 4 -1 0 -1 0 0 0 -1 4 0 0 -1 13 -1 0 0 4. -1 0 0 -1 0 -1 4. 0 0 -1 0 -1 (1) 0 24 2 2 1 2 25 -1 0 - 1 16 (1) Give the matrices L, D, U associated with Jacobi' method and Gauss-Seidel method for solving this system. What is the iteration matrix T, associated with Jacobi's method? What is the iteration matrix Tgs associated with Gauss-Seidel method? (Show your work by hand. You can use MATLAB to calculate matrix inverse (L + D)-7, and you do not need to submit code of this problem.) (5 points) (2) Calculate ||T3||0o and ||TGS||0o. Prove that both Jacobi and Gauss-Seidel iteration con- verges to the solution of this system by combining your results from Problem 2 (1)-(3). (5 points)