1 тақырып. Сызықтық алгебра және аналитикалық геометрия элементтері
Жоспар:
1.Екінші және үшінші ретті анықтауыштар, олардың қасиеттері Алгебралық толықтауыш және минор. Матрица. Матрицаларға амалдар қолдану, кері матрица. Матрица рангісі, оны есептеу. Екі және үш белгісізді екі және үш сызықты теңдеулер жүйесі. Сызықтық теңдеулер жүйесін Крамер ережесі және матрицалық әдіспен шешу. R кеңістігі. R -де векторлардың сызықты тәуелділігі және тәуелсіздігі.
Әдебиет: [1], 4-42 бет. [3], 5-12 бет. [3], 107-122 бет. №1 дәріс
1.Аныктама 1 Екінші ретті анықтауыш деп
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)
санын айтамыз. Бұл сан екі тік және екі жатық жолдардан тұратын
кестесі түрінде белгіленеді және бұл кесте де анықтауыш деп аталады.
Мұндағы - анықтауыштың элементтері. элементінің бірінші
Достарыңызбен бөлісу: |