I already finished the first 1-3, I only need help with question number 4. I am not familiar with matlab and wish to get help with this one question. Thank you!!!!

FINITE ELEMENT TEMPERATURE MINI-PROJECT The finite element method is commonly used for finding the stresses and deflections in an engineering component. It can also be used to find the temperature distribution in a part that is subject to external temperatures. In this example, we will use the technique to find the distribution of temperatures within a flat metal plate, given that the edges of the plate are held at different, but fixed, temperatures. Edge held at 70 deg Temp. distribution in metal plate heated at the edges Edge held at 80 deg Edge held at 65 deg Edge held at 90 deg Here is an example where the inside of the plate has been divided into regions, with 4 "nodes" internal to the plate (nodes are the points where the lines cross). The theory is that the temperatures at these nodes are linear combinations of the temperatures in surrounding nodes. In fact, the relationship is as simple as you might guess: The temperature at any node is the average of the four temperatures that are located directly above, below, to the left, and to the right. Let Ti be the temperature at node i, we get equation: + 70 + T2 +T3) Note this last equation can be rewritten as 4T - T2 - T3 = 135. 1. Find the remaining 3 equations that correspond to the average of the temperatures surrounding nodes 2, 3, and 4 2. You will have a linear system of equations in 4 variables. Write this as an augmented matrix. 3. Solve the system for the 4 temperatures, either by hand (on scrap paper) or using technology. Write the solution here: (Ask yourself if they make sense!) a) Ti = b) T2 = c) T3 = d) TA = 4. As the grid size becomes smaller, the accuracy of the result increases. Many finite element problems can have millions of nodes, and therefore millions of variables and equations. Let's solve the plate problem again, but with 12 nodes: Temp. distribution in metal plate heated at the edges Edge held at 70 deg Edge held at 80 deg Edge held at 65 deg 11 112 Edge held at 90 deg Since you will have 12 variables and 12 equations, you will definitely want to use MATLAB to solve this system quickly. Do that, and write the final temperatures, to two decimal places, next to the corresponding nodes in this figure Temp. distribution in metal plate heated at the edges Edge held at 70 deg Edge held at 80 deg Edge held at 65 deg Edge held at 90 deg Note: ATTACH A SCREENSHOT OF YOUR MATLAB CODE TO THIS SHEET WHEN YOU ARE FINISHED. Note: Make sure to check your answer for correctness! To truly check, you must verify the boldface statement in the middle of page 1