Find the governing equations for the temperatures in the fireplace, furnace, and room, T1, T2, and T3, respectively. Here, q1 is the heat added to the fireplace, q2 is the heat added to the furnace, Ci is the capacitance of a volume, and Ri is the thermal resistance of at a boundary. Assume that Tout, the outside temperature, is an input for to purposes of putting this into matrix input/output form. As your final answer, put the system of equations into matrix input/output form.
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