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Solve Stationary Distribution with Matrix

ku
in Applied Mathematics

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How can I solve the equations above using matrixes to get [math](u_1, u_2, ... , u_8)=\left(\frac{9}{34},\frac{3}{34},\frac{1}{17},\frac{3}{34},\frac{3}{34},\frac{1}{17},\frac{3}{34}, \frac{9}{34} \right)[/math]?

 

I tried substitution but it soon became confusing trying to figure out which I had to substitute with which. Is there a systematic process I can use?

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