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Matrix inversion; temperature node distribution

Please show all the work.

The matrix inversion method has to be shown in detail, the formula used in the class for temperature node distribution was

Tm+1,n + Tm-1, n + Tm, n+1 + Tm, n-1 ? 4Tm,n =0
(where ?m? is the X?axis and ?n? is the Y-axis)

Please see attachment for problem. Thanks.


Solution Summary

The solution is provided in an attachment.