The flexibility matrix for the simply supported beam with reference to the coordinates, as shown below, is
1
\(\rm\frac{L}{6 E I}\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\)
2
\(\rm\frac{L}{3 E I}\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\)
3
\(\rm\frac{L}{6 E I}\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]\)
4
\(\rm\frac{L}{3 E I}\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]\)