The following code generates 100 2 times 2 matrices with Int

The following code generates 100 2 times 2 matrices with Integer coefficients In the ranges k = 1.2, ..., 20. For each fixed k, It finds the percent that are singular. What do the values of the answer percent tell you about the percent of matrices that are singular as k increases? Repeat the experiment for 3 times 3 matrices. What can you say about the percent of singular matrices In this case? What does this indicate about the percent of singular matrices as the sire of the matrix increases?

Solution

a.   Following is one example of values of percent as k increases :
                [33,19,12,10,5,6,1,3,0,5,2,0,0,1,0,2,0,1,0,0]
      We can clearly see, that as k increases, percentage of singluar matrices decreases.

b.   For 3*3 matrix, following is example from one sample run
                [43,15,10,3,3,2,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
      Also in this case, as k increases, percentage of singular matrices decreases
      In this however, percentage decrease rapidly as compared to 2*2 matrices

c.   Thus we can say that as size of matrices increase, decrease in percentage of singular matrices is more rapid