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Systems of Equations with Three Variables

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Given
Π0 = 0.5Π0 + 0.3Π1 +0.2 Π2
Π1 = 0.4Π0 + 0.4Π1 + 0.3Π2
Π2 = 0.1Π0 + 0.3Π1 + 0.5Π2

Where 1 = Π0 + Π1 + Π2

The solution should yield:
Π0 = 21/62
Π1 = 23/62
Π2 = 18/62

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This solution shows how to solve system of equations in three variables.

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Given Π0 = 0.5Π0 + 0.3Π1 +0.2 Π2
We can write it as
0.5Π0 - 0.3Π1 - 0.2 Π2 = 0------------------(i)
Given Π1 = 0.4Π0 + 0.4Π1 + 0.3Π2
We can write it as
-0.4Π0 + 0.6Π1 - 0.3Π2= 0------------------(ii)
Given Π2 = 0.1Π0 + 0.3Π1 + 0.5Π2
We can write it as ...

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