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Node analysis with voltage source in matrix form
. + G_{nn}V_n $$
which in matrix form gives:
$$\begin{bmatrix}I_1 \\ I_2 \\. \\ . \\ . \\ I_n\end{bmatrix} =
\begin{bmatrix} G_{11}& -G_{12}& -G_{13} ... &-G_{1n} \\
-G_{21}& G_{22}& -G_{23} ... … So in matrix form we have(if for example node 1 was connected to an ideal voltage source):
$$\begin{bmatrix}E_1 \\ I_2 \\. \\ . \\ . \\ I_n\end{bmatrix} =
\begin{bmatrix} 1& 0& 0 ... &0 \\
-G_{21}& G_ …