(Solved): The following three tasks describe the problems you are to solve using MATLAB. Task 1. A typical p ...

The following three tasks describe the problems you are to solve using MATLAB. Task 1. A typical problem in thermodynamics is to find the steady-state temperature distribution inside a thin plate if we know the temperature around the boundary. Let T?, T2,..., To be the temperatures in degrees Celsius at the six nodes inside the plate as shown below. 10 10 15 20 25 T? T? T3 ? TA T5 T6 10 20 30 30 The temperature at a node is approximately the average of the four nearest nodes: for instance, (10+15+T?+ T4) 4 T? = 40 Set up a linear system to find the temperature at these six points inside the plate. Then use MATLAB to solve the linear system. In the real world, the approximation becomes better the closer the points are together, which happens as we add more and more points into the grid. This is a situation where we would want to solve linear systems having millions of equations and millions of unknowns. What to turn in: A description of the problem you are solving. You can copy the description from this document. • You need to provide a description of what you are doing at each step. Do not provide just a set of equations and matrices. Explain the reasoning behind the method you are using to create the equations. What is the key concept you are using? The equations will be first written a series of equations, then written in matrix form as Ax = b. Explain how you will be solving this system of equations. Show the MATLAB code used. • The system of equations used to create your A matrix and b vector. The augmented matrix entered into MATLAB. The reduced row echelon form of the augmented matrix. The temperature at each of the unknown points along with the correct units.