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Linear Algebra and its Applications  Circuit
Analysis
One important linear
algebra application
is the resolution of electrical circuits.
We can describe this type of circuits with linear equations, and then
we can solve the linear
system using Matlab.
For
example, let's examine the following electrical circuit (resistors are
in ohms, currents in amperes, and voltages are in volts):
We can describe the circuit with the following system of linear
equations:
7  1(i1  i2)  6  2(i1  i3) = 0
1(i2  i1)  2(i2)  3(i2  i3) = 0
6  3(i3  i2)  1(i3)  2(i3  i1) = 0
Simplifying and rearranging the equations, we obtain:
3i1 +
i2
+ 2i3 = 1
i1  6i2
+ 3i3 =
0
2i1
+ 3i2  6i3 = 6
This system can be described with matrices in the form Ax
= b,
where A
is the matrix of the coefficients of the currents, x
is the vector of unknown currents, and b
is the vector of constants on the right of the equalities.
One
possible Matlab code to solve this is:
A = [3 1 2
1 6
3
2
3 6];
b = [1 0 6]';
i = A\b
The Matlab answer is:
i =
3.0000
2.0000
3.0000
This means that i1
= 3, i2 =
2, and i3
= 3.
Linear Systems  How to Solve them in Matlab Links of interest:
Simultaneous Eq.
Electrical Calculations
Electronic
experiments
Electronic
kits
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