4-- апта. №7. Матрицалар және анықтауштар.
Жүйе коэффициенттерінен тік бұрышты кесте құрауға болады. Ол кестені белгілеуге келесі
символдардың бірін қолданады.
Бұл кестені m жол және n бағаннан тұратын m×n өлшемді матрица деп атайды.
Мұндағы -матрица элеметтері деп атайды. Егер m=n болса, онда (2) кесте
(2*)
түріне ие болады және ол n-ретті квадрат матрица деп аталады. Мұндағы -бас диагональ, -бүйір диагональ элементтері деп аталады.
Дербес жағдайда, n=m=2 болса,
- екінші ретті квадрат матрица болады.
Анықтама :
А матрицаның анықтауышы деп санды аламыз және оны төмендегідей белгілейміз:
![](data:image/png;base64,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)
- екінші ретті анықтауыш,
көріністе жазылып есептелінген кестені үшінші ретті анықтауыш деп аталады.
Анықтауыштардың төмендегі қасиеттерін атап өтуге болады:
10 . Анықтауыштың жолдары мен бағандары орындарын алмастырылса, оның мәні сақталады.
20. Анықтауыштың параллель қатарларын өзара орын алмастырылса, анықтауыш таңбасы өзгереді.
30.
40. =0
50. =0
№8. Матрицаларға қолданылатын амалдар
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