3. The 100m sprint is held at the Olympic Games. The winning times each Olympics are Year (Y) Time (T) Year (Y) Time (T) 1948 10.3 1988 9.92 1952 10.4 1992 9.96 1956 10.5 1996 9.84 1960 10.2 2000 9.87 1964 10.0 2004 9.85 1968 9.95 2008 9.69 1972 10.14 2012 9.63 1976 10.06 2016 9.81 1980 10.25 2020 9.80 1984 9.99 Before you start: You should use a computer to help with this question; do not at- tempt to do the computations by hand. (Hint: The Week 6 lecture notes, page 7, and your answer to Question 5 from Assignment 1, might be useful here). Suppose you had already set up a system of equations for this data using a polynomial of degree 1 (a linear fit). i.e., you had already formed Ax = b, where each equation I was of the form T = CO + CY. You had solved the least squares system using the QR factorization, and that had given you the best fit in terms of the 2-norm (i.e., the least squares solution was the one that minimized || Axb||2), and you found it to be x = [28.1690] -0.0092| But now you were worried that there were outliers in the data set, and you wanted to re-do the computation, but minimizing the 1-norm instead. So, now, you want to solve min || 4x b|| x This problem can be reformulated as an LP: min x,t 1Tt subject to Ax - t