User:Timbatron/matrix

$$ \begin{bmatrix} \dfrac{2 (Z_n - Z_e)}{r - l} & 0 & \dfrac{2 X_e - 2 - r + l}{r - l} & \dfrac{-2 X_e Z_n - Z_e (2 + r - l)} {r - l} \\ 0 & \dfrac{2 (Z_n - Z_e)}{t - b} & \dfrac{2 Y_e - 2 - t + b}{t - b} & \dfrac{-2 Y_e Z_n - Z_e (2 + t - b)}{t - b} \\ 0 & 0 & \dfrac{2 ( 1 - Z_e ) }{Z_f - Z_n} - 1 & \dfrac{2 (Z_e - Z_n)}{Z_f - Z_n} + Z_e \\ 0 & 0 & 1 & -Z_e \end{bmatrix}

$$

Correction 1:

$$ \begin{bmatrix} \dfrac{2 (Z_n - Z_e)}{r - l} & 0 & \dfrac{2 X_e - 2 - r + l}{r - l} & \dfrac{-2 X_e Z_n - Z_e (2 + r - l)} {r - l} \\ 0 & \dfrac{2 (Z_n - Z_e)}{t - b} & \dfrac{2 Y_e - 2 - t + b}{t - b} & \dfrac{-2 Y_e Z_n - Z_e (2 + t - b)}{t - b} \\ 0 & 0 & \dfrac{2 ( Z_f - Z_e ) }{Z_f - Z_n} - 1 & \dfrac{2 Z_n (Z_f - Z_e)}{Z_f - Z_n} + Z_e \\ 0 & 0 & 1 & -Z_e \end{bmatrix}

$$

Correction 2:

$$ \begin{bmatrix} \dfrac{2 (Z_n - Z_e)}{r - l} & 0 & \dfrac{2 X_e - r - l}{r - l} & \dfrac{Z_e (r + l) - 2 X_e Z_n} {r - l} \\ 0 & \dfrac{2 (Z_n - Z_e)}{t - b} & \dfrac{2 Y_e - t - b}{t - b} & \dfrac{Z_e (t + b) - 2 Y_e Z_n}{t - b} \\ 0 & 0 & \dfrac{2 ( Z_f - Z_e ) }{Z_f - Z_n} - 1 & \dfrac{2 Z_n (Z_f - Z_e)}{Z_f - Z_n} + Z_e \\ 0 & 0 & 1 & -Z_e \end{bmatrix}

$$