(Solved):       Let consider a resistive network with node 1,2 and 3 shown in the figure ...

 

 

 

Let consider a resistive network with node 1,2 and 3 shown in the figure below. Figure 1: Triangular Resistive network 4. (10pt) Find the matrices \( D \) and \( \Gamma^{T} \) such that \[ D=\Gamma^{T} L \Gamma \] where \[ D=\left(\begin{array}{ccc} \lambda_{1} & 0 & 0 \\ 0 & \lambda_{2} & 0 \\ 0 & 0 & \lambda_{3} \end{array}\right), \quad \lambda_{1}<\lambda_{2}<\lambda_{3} \]