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1 26. Find the singular values for A = -2 3 and give the matrices I & V for its SVD. 3 2 B) ATA= 1 A" A = -1 3 -1 -2 31 3 3 1-1 14] 2 281 284-4(195) ✓ 22 - 281 + 195 = 0 = 1= -= 14 +1 = 1 = 15, 2 = 13. 2 | 15 0 Σ = 0 V13 0 0 For matrix V of right singular vectors, you need the unit e-vectors for ATA: @2 = 15.(-1 -1}<; = 7-v: ==| __) (A'A – 11)v = [14,1 = v=1l-1 @A = 13(_) 717 = = columns of V are the right singular vectors for A. They give an O.N. basis for Col A. If I had asked for the complete SVD, matrix U is 3x3 with two columns that are the left singular vectors AV +/6, and üz = 102/6, and the third column is üz found easily below. 1 -1 = -1 = 1 AV 3 2 -5 1 1 5) AM fiy üz = - ANz/az =Cl 15 26 U 5 and üz completes an ON basis, so satisfies: V50 VO V50 us=0 0 26. 195 115 u ü, 1 195 ៤ 13 5 1 A = UVT = 1 5 26 7195 0 0 0 V13 0 195