[54pts] : Consider the 2 X 4 matrix _ U 0 2 U A 1 0 U 1 and let T = rank{A). We will work our way toward the Singular Value Decomposition (SVD) of A and to the pseudoinverse of A. a.) Briefly explain why we know, Without having to do any computations, that ATA has at least two eigenvalues equal to D Calculate ATA. [Hint: Only five entries are nonzero] b. Show that det{ATA )J) = A4 6A3 + 319. c. d e. Compute the singular values of A. Label and order them as 01 3 0'2 2 0'3 > 64. J ) J Compute the eigenvalues of ATA. Label and order them as A1 2 A2 2 A3 2 A4. ) l f. What is the matrix 31 for the reduced SVD of A? \"That is the matrix B for the SVD of A? For all of the nonzero eigenvalues of ATA, find corresponding unit eigenvectors. g. h. Compute rref[ATA) and nd the "special solutions". 1. J ) ) Appljg.r the GramSchmidt Process to the vectors you found in part (11). 1.) What is the matrix V1 for the reduced SVD of A? What is the matrix V for the SVD of A? k.) For :i = 1, .. . ,r, compute the vectors 1:1,. 1.] For i = r + 1, . . . ,m, compute the vectors to. If there are no such vectors, briefly explain why. in.) Mat is the matrix U1 for the reduced SVD of A? What is the matrix U for the SVD of A? [1.) What is the matrix 2+ for computing the pseudoinverse of A? 0.) Which matrix multiplication would you perform to compute the pseudoinverse of A