5. Consider the metal plate pictured below, with temperatures listed in "F. We can take temperature measurements at various nodes on the edge of the plate and use these to calculate the temperature at points in the middle of the plate. The temperature at any node can be approximated as the average of the four neighboring nodes. For the first interior node, T_{1}=\frac{10+20+T_{2}+T_{3}}{4} which we can rewrite as 4 T_{1}-T_{2}-T_{3}=30 (a) Write an equation for the other three interior nodes, and set up an augmented matrix for thesystem of equations. (b) [W] Solve the system to find the temperature at each of the nodes.

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