This exercise is similar to the previous one, except this time we will be working with matrices whose entries are real numbers (rather than integers) spread out uniformly randomly in an interval. To generate such an nxn matrix, for example, if we want the entries to be uniformly randomly spread out over (-3, 3), we could use the command 6*rand (n) – 3*ones (n). (a) Run through N = 100 trials of taking the determinant of a 3×3 matrix whose entries are selected uniformly randomly as real numbers in (-3, 3). What was the average value of the determinants? What percent of these 100 matrices were not in vertible? (b) Run through the same experiments with everything the same, except this time let the real number entries be uniformly randomly spread out among -10 through 10. (c) Repeat part (b) except this time using N = 500 trials. (d) Repeat part (c) except this time work with 6×6 matrices. (e) Repeat part (c) except this time work with 10×10 matrices. What general patterns have you noticed? Without doing the experiment.
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