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22η διάλεξη Γραμμικής Άλγεβρας

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Ύπαρξη - Μοναδικότητα - Τάξη 1 - Μετασχηματισμοί

Text of 22η διάλεξη Γραμμικής Άλγεβρας

  • 1. - - 1 - 14 2014

2. 2 9-10 22 () . . 3. 4. Ax = b b A Rm 5. Ax = b b A Rm Ax = b b r = m ( m n) 6. Ax = b b A Rm Ax = b b r = m ( m n) r = m ( m n) A 7. Ax = b b A Rm Ax = b b r = m ( m n) r = m ( m n) A 8. 9. Ax = b b A 10. Ax = b b A Ax = b b r = n ( n m) 11. Ax = b b A Ax = b b r = n ( n m) r = n ( n m) A 12. Ax = b b A Ax = b b r = n ( n m) r = n ( n m) A 13. 14. Ax = b x = Cb 15. Ax = b x = Cb Ax = ACb = b, 16. Ax = b x = Cb Ax = ACb = b, (C). 17. Ax = b x = Cb Ax = ACb = b, (C). Ax = b x = BAx = Bb . 18. A = 4 0 0 0 5 0 19. A = 4 0 0 0 5 0 m = 2,n = 3,r = 2 20. 1 A = 2 1 1 4 2 2 8 4 4 2 1 1 21. 1 A = 2 1 1 4 2 2 8 4 4 2 1 1 = 1 2 4 1 2 1 1 22. 1 A = 2 1 1 4 2 2 8 4 4 2 1 1 = 1 2 4 1 2 1 1 A 1 A = uvT 23. R2 ( ) 24. R2 ( ) Ax x y = Ax 25. R2 ( ) Ax x y = Ax x y = Ax 26. R2 ( ) Ax x y = Ax x y = Ax , .