Jacobi and Gauss-Seidel

1.

Solve exercise 7.4.1(a) on page 308, using two iterations of Jacobi, followed by two iterations of Gauss-Seidel.

2.

Convert this system into the matrix form $\mathbf x_{new} = T \cdot x_{old} + c$, and use matrix operations (in Maple) to perform two more iterations of Jacobi iteration, starting from your solution to the previous question.

3.

Use the eigenvalues command in Maple (it's in the linalg package) to find the spectral radius of T.

4.

Based on the spectral radius, will Jacobi's method converge? What test can we use to determine if Gauss-Seidel will converge? Apply that test and interpret the results.