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14η διάλεξη Γραμμικής Άλγεβρας

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Μη-τετραγωνικοί πίνακες - Υπολογισμός λύσης

Text of 14η διάλεξη Γραμμικής...

  • 1. Grammik 'AlgebraMh-tetragwnik sustmata - Upologismc lsewnTmma Hlektrolgwn Mhqanikn kai Mhqanikn UpologistnPanepistmio Jessalac24 Oktwbrou 2014

2. ProsoqApo ed kai pra qoumen6m 3. 'Anw klimakwtc pnakac'Enac pnakac enai se nw klimakwt morf an 4. 'Anw klimakwtc pnakac'Enac pnakac enai se nw klimakwt morf an lec oi mhdenikc seirc tou brskontai ston ktw mroc tou,kai 5. 'Anw klimakwtc pnakac'Enac pnakac enai se nw klimakwt morf an lec oi mhdenikc seirc tou brskontai ston ktw mroc tou,kai to prto mh-mhdenik stoiqeo kje grammc, to opoolgetai odhg stoiqeo, brsketai sta dexi tou odhgostoiqeou thc prohgomenhc grammc. 6. 'Anw klimakwtc pnakac'Enac pnakac enai se nw klimakwt morf an lec oi mhdenikc seirc tou brskontai ston ktw mroc tou,kai to prto mh-mhdenik stoiqeo kje grammc, to opoolgetai odhg stoiqeo, brsketai sta dexi tou odhgostoiqeou thc prohgomenhc grammc.Pardeigma:2$ 0 $ 0 0 0 $ 0 0 0 0 0 00 0 0 0 0 06666643777775$ = mh-mhdenik stoiqeo odhg stoiqeo, * = otidpotestoiqeo 7. Pardeigma241 3 3 22 6 9 51 3 3 035 8. Pardeigma241 3 3 22 6 9 51 3 3 035 !241 3 3 20 0 3 10 0 6 235 9. Pardeigma241 3 3 22 6 9 51 3 3 035 !241 3 3 20 0 3 10 0 6 235 !241 3 3 20 0 3 10 0 0 035241 3 3 22 6 9 51 3 3 035 10. Pardeigma241 3 3 22 6 9 51 3 3 035 !241 3 3 20 0 3 10 0 6 235 !241 3 3 20 0 3 10 0 0 035241 3 3 22 6 9 51 3 3 035 241 0 02 1 01 2 135 11. Pardeigma241 3 3 22 6 9 51 3 3 035 !241 3 3 20 0 3 10 0 6 235 !241 3 3 20 0 3 10 0 0 035241 3 3 22 6 9 51 3 3 035 241 0 02 1 01 2 135241 3 3 20 0 3 10 0 0 035 12. Paragontopohsh A PLU (n6m)Kje nm pnakac A mpore na analuje seginmeno enc pnaka antimetjeshc P, enc ktwtrigwniko pnaka L me mondec sthn diagnio kaienc nw klimakwto pnaka U. O P kajorzetai apo tic enallagc grammn pouapaite h diadikasa thc apaloifc me odghsh. O L qei touc pollaplasiastc thc apaloifcktw apo thn diagnio. O U ta stoiqea tou A pwc aut prokptounmet thn apaloif. 13. Orismox: lec oi lseic tou Ax b 14. Orismox: lec oi lseic tou Ax bxooo&: lec oi lseic tou Ax 0 15. Orismox: lec oi lseic tou Ax bxooo&: lec oi lseic tou Ax 0x": mia opoiadpote lsh touAx b 16. Orismox: lec oi lseic tou Ax bxooo&: lec oi lseic tou Ax 0x": mia opoiadpote lsh touAx bElejerec metablhtc: lec oisunistsec thc lshc pouden antistoiqon se stlhme odhg. 17. Upologismc Genikeumnhc Lshc Ax b1. Apaloif sto Ax b (Ax b)Ux c) 18. Upologismc Genikeumnhc Lshc Ax b1. Apaloif sto Ax b (Ax b)Ux c)2. Mhdnise tic elejerec metablhtc kai lse(x") 19. Upologismc Genikeumnhc Lshc Ax b1. Apaloif sto Ax b (Ax b)Ux c)2. Mhdnise tic elejerec metablhtc kai lse(x")3. Jse b 0 kai diadoqik, se kje elejerhmetablht 1 jtontac tautqrona tic uploipecmetablhtc sec me 0 kai brec mia omogen lsh(xooo&) 20. Upologismc Genikeumnhc Lshc Ax b1. Apaloif sto Ax b (Ax b)Ux c)2. Mhdnise tic elejerec metablhtc kai lse(x")3. Jse b 0 kai diadoqik, se kje elejerhmetablht 1 jtontac tautqrona tic uploipecmetablhtc sec me 0 kai brec mia omogen lsh(xooo&)4. x x"xooo& 21. A241 3 0 2 10 0 1 4 31 3 1 6 435 22. A241 3 0 2 10 0 1 4 31 3 1 6 435 !241 0 00 1 01 1 135241 3 0 2 10 0 1 4 30 0 0 0 035 23. A241 3 0 2 10 0 1 4 31 3 1 6 435 !241 0 00 1 01 1 135241 3 0 2 10 0 1 4 30 0 0 0 035241 3 0 2 10 0 1 4 30 0 0 0 0352x1x2x3x4x5666643777752435)000 24. A241 3 0 2 10 0 1 4 31 3 1 6 435 !241 0 00 1 01 1 135241 3 0 2 10 0 1 4 30 0 0 0 035241 3 0 2 10 0 1 4 30 0 0 0 0352x1x2x3x4x5666643777752435)000Lseic omogenocs1 23100066664377775, 25. A241 3 0 2 10 0 1 4 31 3 1 6 435 !241 0 00 1 01 1 135241 3 0 2 10 0 1 4 30 0 0 0 035241 3 0 2 10 0 1 4 30 0 0 0 0352x1x2x3x4x5666643777752435)000Lseic omogenocs1 23100066664377775, s2 22041066664377775, s3 21030166664377775 26. A241 3 0 2 10 0 1 4 31 3 1 6 435x 24527 35241 0 00 1 01 1 13524y1y2y335 24527 35 27. A241 3 0 2 10 0 1 4 31 3 1 6 435x 24527 35241 0 00 1 01 1 13524y1y2y335 24527 35 !24y1y2y335 2452035 28. A241 3 0 2 10 0 1 4 31 3 1 6 435x 24527 35241 0 00 1 01 1 13524y1y2y335 24527 35 !24y1y2y335 2452035241 3 0 2 10 0 1 4 30 0 0 0 035266664x1x2x3x4x53777752452035 29. A241 3 0 2 10 0 1 4 31 3 1 6 435x 24527 35241 0 00 1 01 1 13524y1y2y335 24527 35 !24y1y2y335 2452035241 3 0 2 10 0 1 4 30 0 0 0 035266664x1x2x3x4x53777752452035x" 266664x1x2x3x4x537777525020066664377775) 30. x x" xooo& 31. x x" xooo&x c12310006666643777775c22204106666643777775c32103016666643777775 32. x x" xooo&x c12310006666643777775c22204106666643777775c321030166666437777752502006666643777775