Using any version of MATLAB solve the following problem. Please show the code used.

You are given a set of ( , ) data points as follows:

= [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

= [25.6, 27.4, 40.1, 60.2, 66.2, 74.8, 87.9, 94.0, 104.3, 112.3, 132.2, 139.4, 143.0, 153.2, 149.7]

Center the dataset (Subtract the mean from each sample).

Question:

a) Plot the centered datapoints.

b) Compute the covariance matrix.

c) compute the eigenvalues and eigenvectors of the covariance matrix.

d) Now generate a set of random datapoints with 100 samples in a 2-dimensional space. Center the dataset and plot the datapoints.