macierze.pdf - ZESTAW Macierze 1 Wykaza e dana macierz jest...

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ZESTAW Macierze 1. Wykazać, że dana macierz jest nieosobliwa i wyznaczyć macierz odwrotną do niej. Sprawdzić, czy otrzymany wynik jest poprawny. A = 2 0 0 4 0 0 0 1 0 2 0 0 1 0 1 0 B = 2 1 3 0 4 1 1 0 2 2. Korzystając ze wzorów Cramera znaleźć rozwiązania podanych układów równań: a) x y z = 1 3 x + 4 y 2 z = 1 3 x 2 y 2 z = 1 b) y 3 z + 4 v = 0 x 2 z = 0 3 x + 2 y 5 v = 2 4 x 5 z = 0 3. Korzystając z metody eliminacji Gaussa rozwiązać podane układy równań: a) x + y 2 z = 5 2 y + 3 z = 6 x + y 5 z = 3 b) x + y + z = 5 y + z + t = 5 z + t = 3 x + t = 6 c) 3 x 2 y + 5 z + 4 t = 2 6 x 4 y + 4 z + 3 t = 3 9 x 6 y + 3 z + 2 t = 4 4. Rozwiązać równanie: [ 1 1 0 0 1 0 ] [ 0 2 1 1 1 0 ] T X = [ 2 2 1 2 ] 5. Zbadać rozwiązalność układu ze względu na parametr a R : a) x + ( a + 1) y + (2 a + 3) z = 0 2 x + (3 a + 1) y + 10 z = 0 x + 2 y + 5 z = 0
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