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2. Consider a thin metal plate where the temperature (in degree Celsius) around the boundary is known. Introduce a grid as shown in the figure below, so that the metal plate is a collection of 20 point masses (14 of these are on the boundary of the plate and 6 (labelled 1,2,3,4,5 and 6) are in the interior of the plate). You may assume that there is negligible heat flow in the direction perpendicular to the plate. Let T₁, T₂,....Te denote the temperatures at the six interior nodes of the grid in the figure. The temperature at a node is approximately equal to the average of the four nearest nodes. MATH1050/7050 Assignment 2 Due: Wed 4 May, 1 pm 20° 20° 10° 40° 20° 20° 20° (a) (3 marks) Formulate a system of equations for T₁, T2,..., T6. (b) (1 mark) Express the system in the form Az = b. = (c) (1 mark) The solution for the system is T₁ 120/7, T₂ = 150/7, T3 = 190/7, T₁ = 120/7, T = 150/7, T = 190/7. Explain how to solve the equation in (b) to obtain the answers for T₁, T2,..., T6. 10° 20° प m 6 40°