Unformatted text preview: , − 13 .6
13 26 0 −39 2
− 13 In Example 8.4.1, we see that ﬁnding one inverse matrix can enable us to solve an entire family
of systems of linear equations. There are many examples of where this comes in handy ‘in the
wild’, and we chose our example for this section from the ﬁeld of electronics. We also take this
opportunity to introduce the student to how we can compute inverse matrices using the calculator.
6 Note that the solution is the ﬁrst column of the A−1 . The reader is encouraged to meditate on this ‘coincidence’. 500 Systems of Equations and Matrices Example 8.4.2. Consider the circuit diagram below.7 We have two batteries with source voltages
VB1 and VB2 , measured in volts V , along with six resistors with resistances R1 through R6 , measured
in kiloohms, k Ω. Using Ohm’s Law and Kirchhoﬀ’s Voltage Law, we can relate the voltage supplied
to the circuit by the two batteries to the voltage drops across the six resistors in order to ﬁnd the
four ‘mesh’ currents: i1 , i...
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