3 9 The following data matrix contains data on test scores

Last updated: 1/31/2023

3 9 The following data matrix contains data on test scores with x score on first test x score on second test and x3 total score on the two tests X 12 17 29 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 a a2 a3 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