(REQUIRED) Consider a singular value decomposition A=UEVT, where -0.86 -0.11 -0.5 U 0.31 0.68 -0.67 0.41 -0.73 -0.55 = Σ = 12.48 0 0 0 06.34 0 0 0 0 0 0 VE = 0.66 -0.03 -0.35 0.66 -0.13 -0.9 -0.39 -0.13 0.65 0.08 -0.16 -0.73 -0.34 0.42 -0.84 -0.08
(d) (1 point) Use the SVD to determine the rank of A. Explain your reasoning. (e) (2 points) What are the eigenvalues of AT A? Include multiplicity. (f) (2 points) Consider the first term in the singular value decomposition in vector form: -0.86) օլն,vT = 12.48 0.31 (0.66 -0.13 0.65 -0.34] Explain why this is a reasonable approxi- 0.41 mation to the matrix A. How many more terms like this would you need to add to get A exactly? a
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