Chapter 7, Problem 2P

Consider the two-loop circuit shown in Fig P7.2. The currents $l_1$ and $l_2$ (in A) satisfy the following system of equations:

$18l_1-10l_2-246=0$ $(7.86)$ $22l_2-10l_1=-334$ $(7.87)$

(a)Find $l_1$ and $l_2$ using the substitutions method.

(b) Write the system of equations $(7.86)$ and $(7.87)$ in the matrix form $AI=b$, where $I=\left[\begin{array}{c}{I}_1\\ I_2\end{array}\right]$.

(c) Find $l_1$ and $l_2$ using the matrix algebra method. Perform all computations by hand and show all steps.

(d) Find $l_1$ and $l_2$ using the Cramer’s rule.