Question

Найти определитель матричным методом
Методом Крамера
Метод Гауса

Answer 1

1)Матричный метод:
$AX=B\A^{-1}AX=A^{-1}B\X=A^{-1}B$
$left[begin{array}{ccc|ccc|c}2&-1&2&1&0&0&:2\1&1&2&0&1&0\4&1&4&0&0&1end{array}right] textgreater left[begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&downarrow\1&1&2&0&1&0&-1\4&1&4&0&0&1&-4end{array}right] textgreater \ textgreater left[begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&\0&1,5&1&-0,5&1&0&*frac{2}{3}\0&3&0&-2&0&1&end{array}right] textgreater \ textgreater left[begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&0,5\0&1&frac{2}{3}&-frac{1}{3}&frac{2}{3}&0&updownarrow\0&3&0&-2&0&1&-3end{array}right]textgreater$
$left[begin{array}{ccc|ccc|c}1&0&frac{4}{3}&frac{1}{3}&frac{1}{3}&0&\0&1&frac{2}{3}&-frac{1}{3}&frac{2}{3}&0&\0&0&-2&-1&-2&1&:-2end{array}right] textgreater \ textgreater left[begin{array}{ccc|ccc|c}1&0&frac{4}{3}&frac{1}{3}&frac{1}{3}&0&-frac{4}{3}\0&1&frac{2}{3}&-frac{1}{3}&frac{2}{3}&0&-frac{2}{3}\0&0&1&frac{1}{2}&1&-frac{1}{2}&uparrowend{array}right] textgreater \ textgreater$
$left[begin{array}{ccc|ccc|c}1&0&0&-frac{1}{3}&-1&frac{2}{3}&\0&1&0&-frac{2}{3}&0&frac{1}{3}&\0&0&1&frac{1}{2}&1&-frac{1}{2}&end{array}right]$
$left[begin{array}{ccc}-frac{1}{3}&-1&frac{2}{3}\-frac{2}{3}&0&frac{1}{3}\frac{1}{2}&1&-frac{1}{2}&end{array}right]* left[begin{array}{c}3\-4\-3end{array}right] =left[begin{array}{c}-1+4-2\-2-1\frac{3}{2}-4+frac{3}{2}end{array}right]=left[begin{array}{c}1\-3\-1end{array}right]$
2)Метод Крамера:(вложение)
3)Метод Гаусса:
$left[begin{array}{ccc|c|c}2&-1&2&3&downarrow\1&1&2&-4&uparrow\4&1&4&-3&end{array}right] textgreater left[begin{array}{ccc|c|c}1&1&2&-4&downarrow\2&-1&2&3&-2\4&1&4&-3&-4end{array}right] textgreater \ textgreater left[begin{array}{ccc|c|c}1&1&2&-4&\0&-3&-2&11&:-3\0&-3&-4&13&end{array}right] textgreater left[begin{array}{ccc|c|c}1&1&2&-4&\0&1&frac{2}{3}&-frac{11}{3}&\0&-3&-4&13&end{array}right] textgreater \ textgreater left[begin{array}{ccc|c|c}1&1&2&-4&-1\0&1&frac{2}{3}&-frac{11}{3}&updownarrow\0&-3&-4&13&3end{array}right] textgreater$
$left[begin{array}{ccc|c|c}1&1&2&-4&-1\0&1&frac{2}{3}&-frac{11}{3}&updownarrow\0&-3&-4&13&3end{array}right] textgreater left[begin{array}{ccc|c|c}1&0&frac{4}{3}&-frac{1}{3}&\0&1&frac{2}{3}&-frac{11}{3}&\0&0&-2&2&:-2end{array}right] textgreater \ textgreater left[begin{array}{ccc|c|c}1&0&frac{4}{3}&-frac{1}{3}&-frac{4}{3}\0&1&frac{2}{3}&-frac{11}{3}&-frac{2}{3}\0&0&1&-1&uparrowend{array}right] textgreater$
$left[begin{array}{ccc|c|c}1&0&0&1&\0&1&0&-3&\0&0&1&-1&end{array}right]$