Using the Gauss-Seidel method, will the matrix A converge Just came back from my Numerical Analysis midterm, posting up the questions and my solutions for an estimation as to how I did.
If you were to perform the Gauss-Seidel method on a matrix $A$, where 
$$A = \begin{pmatrix}1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 2\end{pmatrix}$$ will it converge?
I was under the impression, from this article, that the method would converge if $A$ is diagonally dominant, that is, the absolute value of each diagonal entry is larger than or equal to the sum of the absolute values of the rest of the row entries.
$|A_{11}| \geq |A_{12}| + |A_{13}| \\ |A_{22}| \geq |A_{21}| + |A_{23}| \\ |A_{33}| \geq |A_{31}| + |A_{32}|$
which for this matrix holds. So I would expect the method to converge to a solution.

This matrix is not strictly diagonal dominant. However, it is irreducible and one of the inequalities is strict, so it is irreducibly diagonal dominant, and Gauß-Seidel should, indeed, converge.
