3.9. The following data matrix contains data on test scores, with x = score on first test, x2 = score on second test, and x3 = total score on the two tests: 12 17 29 X 18 20 38 14 16 30 20 18 38 16 19 35 (a) Obtain the mean corrected data matrix, and verify that the columns are linearly de- pendent. Specify an a' = [a1, a2, 43] vector that establishes the linear dependence. (b) Obtain the sample covariance matrix S, and verify that the generalized variance is zero. Also, show that Sa = 0, so a can be rescaled to be an eigenvector correspond- ing to eigenvalue zero. (c) Verify that the third column of the data matrix is the sum of the first two columns. That is, show that there is linear dependence, with a = 1, a2 = 1, and a3 = -1.