Chapter 7, Problem 8P

A summing Op-Amp circuit is shown in Fig. 7.6. An analysis of the Op-Amp circuit shows that the admittances $G_1$ and $G_2$ in mho $\left(\mho \right)$ satisfy the following system of equations:

$5G_1-145=-10G_2$ $(7.98)$ $-9G_2+71=-4G_1$ $(7.99)$ (a)Find $G_1$ and $G_2$ using the substitutions method.

(b) Write the system of equations $(7.98)$ and $(7.99)$ in the matrix form $AG=b$, where $G=\left[\begin{array}{c}{G}_1\\ G_2\end{array}\right]$.

(c) Find $G_1$ and $G_2$ using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $G_1$ and $G_2$ using the Cramer’s rule.