Correct Answer - Option 4 :

\(\frac{1}{{44}}\left[ {\begin{array}{*{20}{c}} 5&{ - 4}\\ { - 4}&{12} \end{array}} \right]\)
**Explanation:**

If we denote stiffness matrix as M and flexibility matrix as Δ

It is stiffness matrix, and then flexibility matrix is: **Δ = K**^{-1}

**Calculation:**

Δ = \(\frac{1}{{\left( {12\times5 - 4\times4} \right)}}\left[ {\begin{array}{*{20}{c}} 5&{ - 4}\\ { - 4}&{12} \end{array}} \right]\)

**∴ Δ = \(\frac{1}{{44}}\left[ {\begin{array}{*{20}{c}} 5&{ - 4}\\ { - 4}&{12} \end{array}} \right]\)**