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υπολογισμός όλων των λύσεων

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• 1. m n 25 2013

2. - . 3. - . . w v Ax = b 4. - . . w v Ax = b Aw = b Av = b 5. - . . w v Ax = b Aw = b Av = b A(w v ) = 0. 6. Ax = b Ax = b 7. Ax = b Ax = b LUx = b 8. Ax = b Ax = b LUx = b Ux = L1 b 9. Ax = b Ax = b LUx = b Ux = L1 b u b 1 0 0 1 3 3 2 v 1 Ax = LUx = 2 1 0 0 0 3 1 = b2 w b3 1 2 1 0 0 0 0 y 10. Ax = b Ax = b LUx = b Ux = L1 b Ax = LUx = 1 3 3 0 0 3 0 0 0 u b 1 0 0 1 3 3 2 v 1 2 1 0 0 0 3 1 = b2 w b3 1 2 1 0 0 0 0 y u b1 2 v b2 2b1 1 = w 0 b3 2b2 + b1 y 11. x : Ax = b 12. x xoo Ax = b o : Ax = 0 : 13. x Ax = b xoo o : Ax = 0 x : Ax = b : 14. x Ax = b xoo o : Ax = 0 x : Ax = b : . : 15. Ax = b1 Ax = b (Ax = b Ux = c)2 (x )34 b = 0 , 1 0 (xoo o ) x= x + xooo 16. 1 3 0 2 1 A = 0 0 1 4 3 1 3 1 6 4 17. 1 0 0 1 3 0 2 1 1 3 0 2 1 A = 0 0 1 4 3 0 1 0 0 0 1 4 3 1 1 1 0 0 0 0 0 1 3 1 6 4 18. 1 0 0 1 3 0 2 1 1 3 0 2 1 A = 0 0 1 4 3 0 1 0 0 0 1 4 3 1 1 1 0 0 0 0 0 1 3 1 6 4 x1 1 3 0 2 1 x2 0 0 0 1 4 3 x3 = 0 0 0 0 0 0 x4 0 x5 19. 1 0 0 1 3 0 2 1 1 3 0 2 1 A = 0 0 1 4 3 0 1 0 0 0 1 4 3 1 1 1 0 0 0 0 0 1 3 1 6 4 x1 1 3 0 2 1 x2 0 0 0 1 4 3 x3 = 0 0 0 0 0 0 x4 0 x5 3 1 s1 = 0 , 0 0 20. 1 0 0 1 3 0 2 1 1 3 0 2 1 A = 0 0 1 4 3 0 1 0 0 0 1 4 3 1 1 1 0 0 0 0 0 1 3 1 6 4 x1 1 3 0 2 1 x2 0 0 0 1 4 3 x3 = 0 0 0 0 0 0 x4 0 x5 3 2 1 1 0 0 s1 = 0 , s2 = 4 , s3 = 3 0 1 0 0 0 1 21. () 5 5 5 2 LUx = 2 Ly = 2 , Ux = y Ax = 7 7 7 22. ()Ax 1 0 0 0 1 0 1 1 1 5 5 5 2 LUx = 2 Ly = 2 , Ux = y = 7 7 7 5 5 y1 y2 = 2 y1 = 5, y2 = 2, y3 = 0 y = 2 7 0 y3 23. ()Ax 1 0 0 0 1 0 1 1 1 5 5 5 2 LUx = 2 Ly = 2 , Ux = y = 7 7 7 5 5 y1 y2 = 2 y1 = 5, y2 = 2, y3 = 0 y = 2 7 0 y3 5 x1 0 1 3 0 2 1 0 5 0 0 1 4 3 x3 = 2 x1 = 5, x3 = 2 x = 2 0 0 0 0 0 0 0 0 0 0 24. ()x= x +xooo 25. ()x= x +xooo 5 3 2 1 0 1 0 0 = 2+c1 0+c2 4+c3 3 . 0 0 1 0 0 0 0 1