maceirz odwrotna Jack: http://www.wolframalpha.com/input/?i=inverse+of+%7B%7B1,1,-1,-1%7D,%7B5,10,-2,5%7D,%7B-1,2,3,8%7D,%7B3,6,-1,3%7D%7D musze znalezc odwrotna macierz do tej (za pomoca przeksztalcen elementarnych) straszne ulamki mi wychodza...

Saizou : 1 −1 −1 1 | 1 0 0 0 5 10 −2 5 | 0 1 0 0 −1 2 3 8 | 0 0 1 0 3 6 −1 3 | 0 0 0 1 i wykonaj operacje tak, aby po lewejstronie otrzymac macierz jednostkowa

jc: [1 1 −1 −1] [1 0 0 0] [5 10 −2 5 ] [0 1 0 0] [−1 2 3 8 ] [0 0 1 0] [3 6 −1 3 ] [0 0 0 1] [1 1 −1 −1] [1 0 0 0] [2 4 −1 2 ] [0 1 0 −1] [−1 2 3 8 ] [0 0 1 0] [3 6 −1 3 ] [0 0 0 1] [1 1 −1 −1] [1 0 0 0] [2 4 −1 2 ] [0 1 0 −1] [−1 2 3 8 ] [0 0 1 0] [1 2 0 −1 ] [0 −1 0 2] [1 1 −1 −1] [1 0 0 0] [0 0 −1 4 ] [0 3 0 −5] [−1 2 3 8 ] [0 0 1 0] [1 2 0 −1 ] [0 −1 0 2] [1 1 −1 −1] [1 0 0 0] [0 0 −1 4 ] [0 3 0 −5] [−1 2 5 0 ] [0 −6 1 10] [1 2 0 −1 ] [0 −1 0 2] [1 1 0 −5] [1 −3 0 5] [0 0 −1 4 ] [0 3 0 −5] [−1 2 5 0 ] [0 −6 1 10] [1 2 0 −1 ] [0 −1 0 2] [1 1 0 −5] [1 −3 0 5] [0 0 −1 4 ] [0 3 0 −5] [−1 2 5 0 ] [0 −6 1 10] [0 1 0 4 ] [−1 2 0 −3] [1 1 0 −5] [1 −3 0 5] [0 0 −1 4 ] [0 3 0 −5] [−1 2 5 0 ] [0 −6 1 10] [0 1 1 0 ] [−1 −1 0 2] [1 1 0 −5] [1 −3 0 5] [0 0 −1 4 ] [0 3 0 −5] [0 3 5 −5 ] [1 −9 1 15] [0 1 1 0 ] [−1 −1 0 2] [1 1 0 −5] [1 −3 0 5] [0 0 −1 4 ] [0 3 0 −5] [0 0 2 −5 ] [4 −6 1 9] [0 1 1 0 ] [−1 −1 0 2] [1 1 0 −5] [1 −3 0 5] [0 1 1 0 ] [−1 −1 0 2] [0 0 −1 4 ] [0 3 0 −5] [0 0 2 −5 ] [4 −6 1 9] [1 1 0 −5] [1 −3 0 5] [0 1 1 0 ] [−1 −1 0 2] [0 0 −1 4 ] [0 3 0 −5] [0 0 0 3 ] [ ] Coś pomyliłem ... Ale teraz wychodzę

Dziadek Mróz: https://www.symbolab.com/solver/matrix-inverse-calculator/inverse%20%5Cbegin%7Bpmatrix%7D1%261%26-1%26-1%5C%5C%205%2610%26-2%265%5C%5C%20-1%262%263%268%5C%5C%203%266%26-1%263%5Cend%7Bpmatrix%7D

Jack: DZIĘKUJĘ !

Jack: @Saizou, wiem jak to sie robi, ale chodzi mi o to, ze mi straszne ulamki wychodza i nie wiem czy jest sens brnac w to dalej

jc: Macierz Saizou rózni się w jednym miejscu od macierzy z zadania. 1 1 −1 −1 | 1 0 0 0 5 10 −2 5 | 0 1 0 0 −1 2 3 8 | 0 0 1 0 3 6 −1 3 | 0 0 0 1 II −= 2*IV [1, 1, −1, −1] [1, 0, 0, 0] [−1, −2, 0, −1] [0, 1, 0, −2] [−1, 2, 3, 8] [0, 0, 1, 0] [3, 6, −1, 3] [0, 0, 0, 1] IV += 3*II IV = −IV 1 1 −1 −1 | 1 0 0 0 −1 −2 0 −1 | 0 1 0 −2 −1 2 3 8 | 0 0 1 0 0 0 1 0 | 0 −3 0 5 I += IV III −= 3*IV 1 1 0 −1 | 1 −3 0 5 −1 −2 0 −1 | 0 1 0 −2 −1 2 0 8 | 0 9 1 −15 0 0 1 0 | 0 −3 0 5 II += I III += I 1 1 0 1 | 1 −3 0 5 0 −1 0 −2 | 1 −2 0 3 0 3 0 7 | 1 6 1 −10 0 0 1 0 | 0 −3 0 5 III += 3*II 1 1 0 1 | 2 −5 0 8 0 −1 0 −1 | 1 −2 0 3 0 0 0 1 | 4 0 1 −1 0 0 1 0 | 0 −3 0 5 I += II 1 0 0 0 | 3 −7 0 11 0 −1 0 −1 | 1 −2 0 3 0 0 0 1 | 4 0 1 −1 0 0 1 0 | 0 −3 0 5 II += III 1 0 0 0 | 3 −7 0 11 0 −1 0 0 | 5 −2 1 2 0 0 0 1 | 4 0 1 −1 0 0 1 0 | 0 −3 0 5 II = −II III <−> IV 1 0 0 0 | 3 −7 0 11 0 1 0 0 |−5 2 −1 −2 0 0 1 0 | 0 −3 0 5 0 0 0 1 | 4 0 1 −1