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28η και 29η Διάλεξη - Ορίζουσες

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  • 1. 14 2014

2. A, det(A), |A| Rnn R 3. A, det(A), |A| Rnn R 1 4. A, det(A), |A| Rnn R 1 2 5. A, det(A), |A| Rnn R 1 2 3|I | = 1 6. A, B, C 2 1 A 1 B C |A| |B| |C |. 7. A, B, C 2 1 A 1 B C |A| |B| |C |. a + ta c a b c db + tb d +ta c= b d 8. a b c d=c d a b 9. a b c d=c d a b 1 10. a b c d=c d a b 1 1 11. (4-8) 12. (4-8) 13. (4-8) 14. (4-8) 15. (4-8) A |A| = 0 16. , |A| = |U| |A| = ( ) . 17. (9, 10) 18. (9, 10) 19. (9, 10) 20. (9, 10) : . 21. Cij = (1)(i+j) det Aij aij Aij (n 1) (n 1) A i- j- . 22. Cij = (1)(i+j) det Aij aij Aij (n 1) (n 1) A i- j- . (1)(i+j) : 23. Cij = (1)(i+j) det Aij aij Aij (n 1) (n 1) A i- j- . (1)(i+j) : + + + + + . . . . .. . . . . . . . 24. ( ), i- |A| = ai,1 Ci,1 + ai,2 Ci,2 + . . . + ai,n Ci,n 25. ( ), i- |A| = ai,1 Ci,1 + ai,2 Ci,2 + . . . + ai,n Ci,n ( ) . 26. 2 3 4 A = 0 4 2 1 1 5 27. 2 3 4 2 4 A = 0 4 2 = C22 = + det 1 5 1 1 5 28. 2 3 4 2 4 A = 0 4 2 = C22 = + det 1 5 1 1 5C23 = det2 3 1 1 29. 2 3 4 2 4 A = 0 4 2 = C22 = + det 1 5 1 1 5 C22 = 2 5 (4) 1 = 14C23 = detC23 = (2 (1) 3 1) = 52 3 1 1 30. 2 3 4 2 4 A = 0 4 2 = C22 = + det 1 5 1 1 5 C22 = 2 5 (4) 1 = 14C23 = det2 3 1 1C23 = (2 (1) 3 1) = 5det A = a21 C21 + a22 C22 + a23 C23 = 0? + (4) 14 + 2 5 = 46 31. A1 A1 |A| 32. A1 A1 |A| A1 =Asymp |A|