Chapter 2.5, Problem 1E

Compute the first two steps of the Jacobi and the Gauss-Seidel Methods with starting vector [0,…,0].

a. $\left[\begin{array}{cc}3& -1\\ -1& 2\end{array}\right]\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}5\\ 4\end{array}\right]$

b. $\left[\begin{array}{ccc}2& -1& 0\\ -1& 2& -1\\ 0& -1& 2\end{array}\right]\left[\begin{array}{c}u\\ v\\ w\end{array}\right]=\left[\begin{array}{c}0\\ 2\\ 0\end{array}\right]$

c. $\left[\begin{array}{ccc}3& 1& 1\\ 1& 3& 1\\ 1& 1& 3\end{array}\right]\left[\begin{array}{c}u\\ v\\ w\end{array}\right]=\left[\begin{array}{c}6\\ 3\\ 5\end{array}\right]$