$($a$)$ Write the node$-$voltage equations in matrix form for the circuit of Figure $3,$ and explain how the process would have to change if the $3\mathrm{.}5$ A current source was replaced with a $3\mathrm{.}5$ V voltage source.

Figure $3$: Circuit for node$-$voltage analysis

$($b$)$ Explain how capacitive sensing works, and give two examples of its application.

$($c$)$ An antenna pointing system $($APS$)$ is used to align an antenna to a satellite for transmitting and receiving data. Both the yaw and pitch of the APS are being controlled by an external motor. Explain how voltage divider$-$based transducers could be used to verify that the correct yaw and pitch angles are being set by the controller.