Please assist in this homework practical. Please also provide screenshots of R outputs and code for extra practice.

Consider the two following observed data sets with 5 observations and 2 variables for A data set and 3 variables for B 4 6 3 6 0 6 A = 6 2 B = 0 3 2 3 3 6 3 9 3 The eigenvalues and corresponding eigenvectors of the data B are given as follows Al = 14.196, el = (-0.57735, -0.21132, -0.78868), A2 = 3.804, 62 = (0.57735, -0.78868, -0.211324) A3 = 0, 62 = (-0.57735, -0.57735, 0.57735) T (a) (1 Marks) Why is not possible to get a spectral decomposition of the data set A? (b) (1 Marks) What is the possible rank of the matrix A? What is the possible rank of the matrix B? (c) (1 Marks) Check your answer by using the R function rankMatrix from the package Matrix. (d) (2 Marks) Using the above eigenvalues and eigenvectors of the ma- trix B, write down the singular value decomposition expression for B. Check the results by reconstructing B using the SVD decomposition. (e) (2 Marks) Using R provide the singular decomposition of the matrices A. Check the result by reconstructing A using the SVD decomposition. Now work with the data set A. Let A = [a,, a2, a;], a = [a1, a2, a;] and 1 = [1, 1, 1, 1, 1, 1] be the data matrix, sample mean column vector and all-ones column vector, respectively