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#quExample - Electronics application of 3×3 System of Equations

Find the electric currents shown by solving the matrix equation (obtained using Kirchhoff''s Law) arising from this circuit:

math expression

??I1+I2+I3-2I1+3I2-3I2+6I3??=??0240??

Answer

We can write this as:

??1-2013-3106????I1I2I3??=??0240??

So we have:

??I1I2I3??=??1-2013-3106??-1??0240??

Using a computer algebra system to perform the inverse and multiply by the constant matrix, we get:

I1=-6 A

I2=4 A

I3=2 A

We observe that I1 is negative, as expected from the circuit diagram.
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