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<tex> \begin{vmatrix} x_5 \\ x_6 \\ x_7 \\ x_8 \end{vmatrix} = \begin{vmatrix} y_5+z_5 \\ y_6+z_6 \\ y_7+z_7 \\ y_8+z_8 \end{vmatrix} = \begin{vmatrix} y_5+z_5 \\ \lambda y_5+ \mu z_5 \\ y_7+z_7 \\ \alpha y_7+ \beta z_7 \end{vmatrix} = \begin{vmatrix} y_5 \\ \mu z_5 \\ y_7 \\ \beta z_7 \end{vmatrix} + \begin{vmatrix} y_5 \\ \mu z_5 \\ z_7 \\ \alpha y_7 \end{vmatrix} + \begin{vmatrix} z_5 \\ \lambda y_5 \\ y_7 \\ \beta z_7 \end{vmatrix} + \begin{vmatrix} z_5 \\ \lambda y_5 \\ z_7 \\ \alpha y_7 \end{vmatrix} = </tex>
<tex> = \mu (\beta - \alpha) \begin{vmatrix} y_5 \\ z_5 \\ y_7 \\ z_7 \end{vmatrix} - \lambda ( \beta- \alpha) \begin{vmatrix} y_5 \\ z_5 \\ y_7 \\ z_7 \end{vmatrix} = ( \mu - \lambda)( \beta- \alpha) \begin{vmatrix} a_{51} & a_{52} & 0 & 0 \\ 0 & 0 & a_{53} & a_{54} \\ a_{71} & a_{72} & 0 & 0 \\ 0 & 0 & a_{73} & a_{74} \end{vmatrix} = </tex>
<tex>( \mu - \lambda)( \beta- \alpha) \begin{vmatrix} a_{51} & a_{52} \\ a_{71} & a_{72} \end{vmatrix} \begin{vmatrix} a_{53} & a_{54} \\ a_{73} & a_{74} \end{vmatrix} = 0</tex>