Singular Matrices The following code generates 100 2 times 2 matrices with integ
ID: 3031866 • Letter: S
Question
Singular Matrices 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. percent = zeros (1, 20) ' ; for k = 1 : 20 for i = 1 : 100 if det(floor((2*k + 1)*rand(2) - k)) ==0 percent (k) = percent (k) + 1; end end end percent 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 size of the matrix increases?Explanation / Answer
(a)
Columns 1 through 16:
42 25 11 7 3 7 3 4 1 2 4 1 3 0 0 1 Columns 17 through 20: 0 1 0 1
As k increases, percent singular matrices decreases.
(b)
Columns 1 through 16:
46 18 12 1 4 1 0 2 0 0 0 1 0 0 0 0 Columns 17 through 20:
0 0 0 0
As k increases, percent singular matrices decreases.
(c)
With increasing size, percent is usually less for larger size matrix