$4\mathrm{.}8$ Consider a two$-$port network, and let Z$(1)$

SC$,$ Z$(2)$

SC$,$ Z$(1)$

OC$,$ and Z$(2)$

OC be the input impedance seen

when port $2$ is short$-$circuited, when port $1$ is short$-$circuited, when port $2$ is open$-$circuited, and

when port $1$ is open$-$circuited, respectively. Show that the impedance matrix elements are given by

Z$11=$ Z$(1)$

OC$,$ Z$22=$ Z$(2)$

OC$,$ Z$2$

$12$

$=$ Z$2$

$21$

$=$

Z$(1)$

OC

$$ Z$(1)$

SC

Z$(2)$

OC$.$