Question

6. Find a full SVD of A [101 이 0 1 0 1 임

Answer 1

solution- Given * For A10:0) *100] [1:26:] A. A A:A': Eigen rectors for A.A-dal=0 A. A': 1(2-1) o (22.0 (2-1) (2-1)(2-)) - 0X0-0 4 - 4A +4²0 1241 +420 (al - 2) (4-2): 0 1=2, 2 eigen values of A.A Ford=2 Eigen vectors. v=[ o ] s vz (0) for eigen vector -1 (0-1), length 1:10 +12 = 1 so, normalizing giver (:, +).(0,0) for eigen vector -2 (10), length - 12+02 = 1 so, normarlizing gives 42 = (,0)= (1,0) La Total 1st solutim

* for A. A : A. A : - 0 :::::::::: ۵ 0 - - - A! A Eigen vectors for AA - A1) 0 و ( -) ا 0 (1-4) 0 و (4-1) (1-) - (-) * ه (-1) ه (-) و (1) ه ا * و + ه (-1) | (7-1) 0 ہ ((-)) (۷۱) :: +OX مے ۵ 0 0 - 0: (و) رو + (12-28) + (0) رو + (13-44382 2- (1-1) + 24 + 54-413++) +6+ (24-49) + 0 = 0 4 483 480 - 2:03 A-28 د و= (2-CA(-۸)2( که ما eigen volwy : ام 09 م م ه / امم A: 2 V: Eigen vectores are [] . ده ر

(-0.7071, 0, 0.7071, 0) Total and solution So, from solution: o 1.4142 o o o O LE 0 O O 1.41 42 52 O O (4.,42) - O vis found using formule ve I A. up O -0.7071 0.7071 :: V- a 0.7071 -0.7071 0-70 71 0.707) -0.7071 o 0.7071 from 2nd solation 14142 lo 1 : 1 لب 52 1.4142 -0.707) o 0.7071 = [VV2,13,14 ] o -0.70 71 0.70 71 0.7071 O 0.7071 0.70 71 10.70 71 U is found using formula qq a t cu А 05 U=:] 8+ verify lat solution AL UEVT solution id possible Verify solution A = VEUT and solution ġ oso possible put * Thanks YOU