Question: The linear system x 1 + 2x 2 2x 3 = 7, x 1 + x 2 + x 3 = 2, 2x 1

The linear system x1 + 2x2 − 2x3 = 7, x1 + x2 + x3 = 2, 2x1 + 2x2 + x3 = 5, has the solution (1, 2,−1)t .

a. Show that ρ(Tj) = 0.

b. Use the Jacobi method with x(0) = 0 to approximate the solution to the linear system to within 10−5 in the l∞ norm.

c. Show that ρ(Tg) = 2.

d. Show that the Gauss-Seidel method applied as in part (b) fails to give a good approximation in 25 iterations.

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