Discussion
If \(Z_{11} = 2\,\Omega\), \(Z_{12} = 1\,\Omega\), \(Z_{21} = 1\,\Omega\), \(Z_{22} = 3\,\Omega\). What is the determinant of admittance matrix ?
Answer: D
The determinant of the admittance matrix is 1/5, because the admittance matrix is the inverse of the impedance matrix and the determinant of an inverse is the reciprocal of the determinant. Here the impedance matrix is
\[ Z = \begin{bmatrix} 2 & 1 \\ 1 & 3 \end{bmatrix} \]
\[ \Delta_Z = (2)(3) - (1)(1) = 5 \]
\[ Y = Z^{-1} \]
\[ \Delta_Y = \frac{1}{\Delta_Z} = \frac{1}{5} \]
The value 5 is the determinant of the impedance matrix and not of the admittance matrix, which is the likely slip. The values 0 and 1 do not arise from these figures, since 0 would mean the matrix cannot be inverted. The answer is 1/5.
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