Suppose that M is an 8 x 3 matrix. Let A be the matrix consisting of the first and second columns of M and let B be the matrix consisting of the second and third columns of M Suppose the k-means algorithm finds 2 clusters for matrix A and produces a cluster vector a Suppose the k-means algorithm finds 2 clusters for matrix B and produces a cluster vector b. Suppose that in both cases, the k-means algorithm actually succeeds in optimizing the objective func- tion. The examples that you create below should be drawn by hand without using R. Choose examples so that it is easy for a human to determine unique clusters. (a) Give an example of actual numeric entries in M where the cluster vectors a and b are the same. State the actual cluster vectors and draw plots to illustrate. (b) Give an example of actual numeric entries in M where the cluster vectors a and b differ in just one entry. State the actual cluster vectors and draw plots to illustrate. Suppose that M is an 8 x 3 matrix. Let A be the matrix consisting of the first and second columns of M and let B be the matrix consisting of the second and third columns of M Suppose the k-means algorithm finds 2 clusters for matrix A and produces a cluster vector a Suppose the k-means algorithm finds 2 clusters for matrix B and produces a cluster vector b. Suppose that in both cases, the k-means algorithm actually succeeds in optimizing the objective func- tion. The examples that you create below should be drawn by hand without using R. Choose examples so that it is easy for a human to determine unique clusters. (a) Give an example of actual numeric entries in M where the cluster vectors a and b are the same. State the actual cluster vectors and draw plots to illustrate. (b) Give an example of actual numeric entries in M where the cluster vectors a and b differ in just one entry. State the actual cluster vectors and draw plots to illustrate