Let S denote the set of all 2 × 2 matrices A such that the iterative sequence generated by the Gauss-Seidel method applied to the system of linear equations \(\rm A\begin{pmatrix}x_1\\\ x_2\end{pmatrix}=\rm \begin{pmatrix}2\\\ 3\end{pmatrix}\) converges for every initial guess. Then which of the following statements are true?
1
\(\rm \begin{pmatrix}5&8\\\ 1&2\end{pmatrix}\in S\)
2
\(\rm \begin{pmatrix}3&2\\\ 1&2\end{pmatrix}\in S\)
3
\(\rm \begin{pmatrix}-3&1\\\ 2&3\end{pmatrix}\in S\)
4
\(\rm \begin{pmatrix}2&2\\\ 4&3\end{pmatrix}\in S\)