Lesson 5

Problem. Let \[G([4], \{\{1, 2\}, \{2, 3\}, \{3, 4\}, \{4, 1\}\})\] be a 4-cycle. Its Tutte matrix is \[\begin{pmatrix}0 & x_{12} & 0 & x_{14} \\ -x_{12} & 0 & x_{23} & 0 \\ 0 & -x_{23} & 0 & x_{34} \\ -x_{14} & 0 & -x_{34} & 0\end{pmatrix}.\] Compute the determinant of this matrix and enter it assuming that \(a = x_{12}, b = x_{14}, c = x_{23}, d = x_{34}\).