One step Gauss Seidel method Apply one step of the Gauss Seidel method to $A\textbf{x} = b$ with 
A = $\begin{bmatrix} 
4 & 2 & 1 \\ 
1 & 4 & 1 \\ 
1 & 2 & 4  
\end{bmatrix}$, b = $\begin{bmatrix} 
4\\ 
5\\ 
8 
\end{bmatrix}$ $x_{0}$ = $\begin{bmatrix} 
64\\ 
64\\ 
-128 
\end{bmatrix}$
Does the method converge to the solution? 
To answer the question, this is what I did... 
$$x_{1} = \frac{4 - 2x_{2} - x_{3}}{4} => x_{1} = \frac{4-2(64)+128}{4} = 1$$
$$x_{2} = \frac{5-x_{1}-x_{3}}{4} = \frac{5-1+128}{4} = 33$$
$$x_{3} = \frac{8-x_{1}-2x_{2}}{4} = \frac{8-1-66}{4} = -59/4$$ 
Did I do it right? If not I am confused. Can someone help me do this correct? Thanks. 

Yes, your first iteration is correct.  Here are some iterates and details.
Iteration 1:
$$\left(
\begin{array}{cccccccccc}
 1. \\ 33.  \\ -14.75 
\end{array}
\right)$$
Iteration 2:
$$\left(
\begin{array}{cccccccccc}
-11.8125  \\ 7.89063  \\ 1.00781 
\end{array}
\right)$$
Iteration 3:
$$\left(
\begin{array}{cccccccccc}
-3.19727  \\ 1.79736  \\ 1.90063 
\end{array}
\right)$$
... Iteration 10:
$$\left(
\begin{array}{cccccccccc}
0.208341 \\ 0.812503 \\ 1.54166
\end{array}
\right)$$
You can compare this against the actual result of:
$$x = \left(
\begin{array}{c}
 \frac{5}{24} \\
 \frac{13}{16} \\
 \frac{37}{24} \\
\end{array}
\right) = \left(
\begin{array}{c}
 0.208333 \\
 0.8125 \\
 1.54167 \\
\end{array}
\right)$$
