The thermal expansion of a metal alloy at different temperatures are shown in Table II Your goal is to find the thermal expansion of the alloy at 45 degrees. Write MATLAB codes to answer the following a) Obtain the linear Lagrange polynomial expressions and determine the estimated thermal expansion values for each temperature given. Then, determine the maximum and average errors across all data points. Plot all the data points and the polynomial on a single figure Il Linear Lagrange Polynomial Fit utilizes the two c value) Table II. Instantaneous thermal expansion at different temperatures Temperature Instantaneous Thermal CF) 80 60 40 20 Expansion -in/in/oF) 6.47 6.36 6.24 6.12 6.00