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x(k)=(b(k)-U(k,k+1:n)*x(k+1:n))/U(k,k);
end
x

8.7 Application of Matrix Methods

This section provides seven representative applications that illustrate the
immense power that matrix formulation and tools can provide to diverse
problems of common interest in electrical engineering.

8.7.1 dc Circuit Analysis

Example 8.6
Find the voltages and currents for the circuit given in Figure 8.1.

50 Ω 100 Ω
V 1 V 2 V 3
I 1 I 2
I 3
5 V 300 Ω Lamp
R L

FIGURE 8.1
Circuit of Example 8.6.

Solution: Using Kirchoff’s current and voltage laws and Ohm’s law, we can
write the following equations for the voltages and currents in the circuit,
assuming that R = 2Ω:
L
V = 5
1
V − V = 50 I
1 2 1
V − V = 100 I
2 3 2
V = 300 I
2 3
V = I 2
3 2
I = I + I
1 2 3

© 2001 by CRC Press LLC