We can use methods from linear algebra to find fits for various functions through data points, and learn about the nature of such fits. Use the digits of your stu- dent number to construct five numbers in the following way: if the digits are dd2d3d4d5d6d7, write down the two-digit numbers y = d2d3, y2 = d3d4, y3 = d4d5, y4d5d6 and y5=d6d7. So, for example, if your student number was 5123406, your numbers would be y = 12, y2 = 23, y3 = 34, y4 = 40 and y5 = 066. If your student number has fewer than seven digits, pre-pad it with Os (so 12345 becomes 0012345). Now consider the five points A = (-2, y), B = (-1, y2), C = (0, y3), D = (1, y4) and E=(2, y5). (a) In this first part, you must find the polynomial that passes through points A, B, C, D and E. (i) Set up a system of equations to find the unknown coefficients ao, a1, a2, a3 and a4 for the polynomial y = ax + 3x + ax + ax + ao that passes through A, B, C, D and E. (ii) Solve this system of equations to find the unknown coefficients. (iii) Confirm that the resulting polynomial does indeed pass through the required points.