Chapter 7, Problem 4P

Consider the two-node circuit shown in Fig P7.4. The voltages $V_1$ and $V_2$ (in A) satisfy the following system of equations: $4V_1-V_2=20$ $(7.90)$ $-3V_1+8V_2=40$ $(7.91)$

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

(b) Write the system of equations $(7.90)$ and $(7.91)$ 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.