Chapter 7, Problem 7P

An Analysis of the circuit shown in Fig P7.7. yeilds the following system of equations: $-4V_2+7V_1=0$ $(7.96)$ $2V_1-7V_2+10=0$ $(7.97)$

(a)Find $V_1$ and $V_2$ using the substitutions method.

(b) Write the system of equations $(7.96)$ and $(7.97)$ in the matrix form $AV=b$, where $V=\left[\begin{array}{c}{V}_1\\ V_2\end{array}\right]$.

(c) Find $V_1$ and $V_2$ using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $V_1$ and $V_2$ using the Cramer’s rule.