examples - ÇÆ Ì ÊÅÁÆ Æ̸ Å Æ ÇÅÈÍÌ...

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Unformatted text preview: ÇÆ Ì ÊÅÁÆ Æ̸ Å Æ ÇÅÈÍÌ ÌÁÇÆË Ä Ø³× ÓÑÔÙØ det(A) × × Ú Ö Ð Û Ý׺ 0 3 A= 6 3 1 1 0 1 4 4 2 6 32 40 32 60 ½º ÓÒ× ÖØ Ø ÖÑ ÒØ ÊÓÛ ÓÔ ØÓ ÊÓÛ ÐÓÒ 1 1 0 1 4 4 2 6 32 40 = 32 60 0 1 1 1 2 4 4 6 0 3 6 3 32 40 32 60 1 1 0 1 4 4 2 6 32 40 . 32 60 ÇÙÖ Ö×Ø Ñ Ø Ó ØÓ ÓÑÔÙØ Ø × × ØÓ ÖÓÛ¹Ö Ù ØÓ ÐÓÒ ÓÖѸ Û Ø Ø 0 3 6 3 1 1 0 1 4 4 2 6 32 40 32 60 = 6 3 (−1) 0 3 1 3 (−6) 0 3 1 0 (−6) 0 0 1 0 (−6) 0 0 1 0 (−6) 0 0 1 0 (−24) 0 0 0 3 det 6 3 Ð Ò Ø ÖÑ× ÐÐ 1. R1 ← R3 = 1 0 3 16 3 1 4 40 1 4 32 1 6 60 1 R1 ← R1 6 = 0 1 16 3 3 1 3 24 1 4 32 1 5 44 1 0 3 16 3 1 3 24 018 0 2 20 R2 ← R2 − 3R1 R4 ← R4 − 3R1 = R3 ← R3 − R2 R4 ← R4 − R2 = 0 1 16 3 3 1 3 24 018 004 1 0 3 16 3 1 3 24 018 001 −24 R4 ← R4 − 2R3 = = 1 R4 ← R4 4 ½ ÇÆ Ì ÊÅÁÆ Æ̸ Å Æ ÇÅÈÍÌ ÌÁÇÆË ¾ ¾º ÁØ × ×Ö Û ÓÒ³Ø Ñ Ø ÊÓÛ ÓÔ ØÓ ÍÔÔ Ö ÌÖ Ò ÙÐ Ö Ð Ò Ø ÖÑ× 1. Ò Û Ø ÖÓÛ ÓÔ Ö Ø ÓÒ׸ ÙØ ÚÓ Ò Ö Ø ÓÒ׺ 0 3 6 3 1 1 0 1 4 4 2 6 32 40 32 60 = 6 3 (−1) 0 3 3 3 (−2) 0 3 3 0 (−2) 0 0 3 0 (−2) 0 0 3 0 (−2) 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 2 4 4 6 1 4 4 6 1 3 4 5 32 40 32 60 16 40 32 60 16 24 32 44 R1 ← R3 = 1 R1 ← R1 2 = R2 ← R2 − R1 R4 ← R4 − R1 = 1 16 3 24 18 2 20 1 16 3 24 18 04 R3 ← R3 − R2 R4 ← R4 − R2 = = = R4 ← R4 − 2R3 (−2)(3)(1)(1)(4) −24 ¿º Ï Ò ÜÔ Ò ÓÒ Ø ÜÔ Ò Ò ×Ø Ô ÐÓÒ ÊÓÛ × ÓÒ ÖÓÛ¸ Ø ÇÆ Ì ÊÅÁÆ Æ̸ Å Æ ÇÅÈÍÌ ÌÁÇÆË ¿ 0 3 6 3 1 1 0 1 4 4 2 6 32 40 32 60 1 1 0 1 4 4 2 6 32 40 32 60 + 0 3 6 3 1 1 0 1 4 4 2 6 32 40 32 60 0 3 −4 6 3 32 32 60 1 1 0 1 4 4 2 6 32 40 32 60 0 3 + 40 6 3 1 1 0 1 4 32 4 40 2 132 6 60 0 3 = −3 6 3 1 4 32 0 4 32 01 = −3 0 2 32 + 6 2 32 − 4 6 0 1 6 60 3 6 60 31 1 4 32 1 4 32 = −3 2 0 1 16 − 32 0 1 16 1 6 60 1 6 60 0 4 32 0 4 32 + −6 3 1 16 + 2 3 1 16 − 32 3 6 60 3 6 60 0 1 32 0 1 32 −4 −6 3 0 16 − 32 3 0 16 3 1 60 3 1 60 014 014 +40 −6 3 0 1 − 2 3 0 1 316 316 = −3 2 −4 −6 1 32 1 60 − 32 − 32 14 16 + −6 014 + 40 6 0 2 316 0 4 32 3 1 16 3 6 60 4 32 6 60 +2 0 32 3 60 01 31 − 32 04 36 1 32 1 60 01 31 + 40 −6 14 16 −2 = −3 (2(28) − 32(2)) + (−6(48) + 2(−96) − 32(−12)) −4 (−6(28) − 32(−3)) + 40 (−6(2) − 2(−3)) = −3 (−8) + (−96) − 4 (−72) + 40 (−6) = −24 ÁØ × ÒÓØ Ù×ØÓÑ ÖÝ ØÓ ÛÖ Ø ÓÛÒ Ø Ñ ØÖ × Û Ø Ø Ø ÓÙ Ø ÓÒ ÓÑÔÐ Ø Ü ÑÔÐ ÛÓÙÐ ÐÔ ÝÓÙº º ÖÓ×× ÓÙØ ÖÓÛ Ò ÓÐÙÑÒº Á Ù×Ø Å Ü Ò ÊÓÛ Ò ÓÐÙÑÒ ÇÔ Ö Ø ÓÒ× Û Ø ÜÔ Ò× ÓÒ ÐÐ ÝÓÙ Û ÒØ × Ø × ØÓ Ö Ø ÐÓØ× Ó ÓÐÙÑÒ ÓÔ Ö Ø ÓÒ× ÛÓÖ Ù×Ø Ð ÖÓÛ ÓÔ Ö Ø ÓÒ× ÓÖ Ø ÖÑ Ò Òظ Ò ÝÓÙ × Ô ØØ ÖÒ× Ò Ø ÓÐÙÑÒ׸ Ø Þ ÖÓ× ×Ó ÜÔ Ò Ò × ÒÓØ ×Ó Ô Ò Ùк ÁÒ Ø × ÓÑÔÙØ Ø ÓÒ¸ Á Ó • ØÝÔ ÁÁ ÓÐÙÑÒ ÓÔ Ö Ø ÓÒ ´C 1 ← 1 C 1µ 3 • ØÝÔ ÁÁÁ ÖÓÛ ÓÔ Ö Ø ÓÒ ´R2 ← R2 − R1µ Ø ÖÑ Ò ÒØ׺ ËÓ Ú ÒØ º Ì ÇÆ Ì ÊÅÁÆ Æ̸ Å Æ ÇÅÈÍÌ ÌÁÇÆË • ØÝÔ ÁÁÁ ÓÐÙÑÒ ÓÔ Ö Ø ÓÒ ´C 4 ← C 4 − 8C 1µ • ÜÔ Ò ÐÓÒ Ø × ÓÒ ÖÓÛ • ÜÔ Ò ÐÓÒ Ø × ÓÒ ÖÓÛ 0 3 6 3 1 1 0 1 4 4 2 6 32 40 32 60 0 1 =3 2 1 0 1 =3 2 1 0 1 =3 2 1 1 1 0 1 1 0 0 1 1 0 0 1 4 4 2 6 32 40 32 60 4 32 08 2 32 6 60 4 32 00 2 16 6 52 1 4 32 = −3 0 2 16 1 6 52 = −3 2 16 6 52 + 4 32 2 16 = −3 (8 − 0)) = −24 ...
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