Матрично уравнение

[mimi21]

помагайте

2 -1 1 1 2 0
0 1 3 .Х = -1 0 2
1 1 1 3 1 1

[Реклама]

[chuhoveca]

2 -1 1 | 1 2 0 ~ 1 -2 0 | -2 1 -1 ~ 1 0 6 |-4 1 3 ~ 1 0 6 | -4 1 3 ~ 1 0 0 |-4 1 3
0 1 3 |-1 0 2 ~ 0 1 3 | -1 0 2 ~ 0 1 3 |-1 0 2 = 0 1 3 | -1 0 2 ~ 0 1 0 |-1 0 2 =
1 1 1 | 3 1 1 ~ 1 1 1 | 3 1 1 ~ 0 3 1 | 5 0 2 ~ 0 0 -8| 8 0 -4 ~ 0 0-8 | 8 0 -4

~1 0 0|-4 1 3 -4 1 3
~0 1 0|-1 0 2 => -1 0 2 е отговора, ако съм объркал се извинявам, ако не съвпада
~0 0 1|-1 0 1/2 -1 0 1/2

отговора я умножи х2 и ще стане -8 2 6
-2 0 4
-2 0 1

[nikko1]

[tex]\left(\begin{array}{ccc|ccc}2&-1&1&1&2&0\\0&1&3&-1&0&2\\1&1&1&3&1&1\end{array}\right)\longright^{R_1-R_3}\left(\begin{array}{ccc|ccc}1&-2&0&-2&1&-1\\0&1&3&-1&0&2\\1&1&1&3&1&1\end{array}\right)\longright^{R_3-R_1}\left(\begin{array}{ccc|ccc}1&-2&0&-2&1&-1\\0&1&3&-1&0&2\\0&3&1&5&0&2\end{array}\right)\longright^{R_1+2R_2}_{R_3-3R_2}\left(\begin{array}{ccc|ccc}1&0&6&-4&1&3\\0&1&3&-1&0&2\\0&0&-8&8&0&-4\end{array}\right)\longright^{-\frac{1}{8}R_3}\left(\begin{array}{ccc|ccc}1&0&6&-4&1&3\\0&1&3&-1&0&2\\0&0&1&-1&0&1/2\end{array}\right)\rightarrow[/tex]

[tex]\longright^{R_1-6R_3}_{R_2-3R_1}\left(\begin{array}{ccc|ccc}1&0&0&2&1&0\\0&1&0&2&0&1/2\\0&0&1&-1&0&1/2\end{array}\right).[/tex]

Отговор: [tex]X=\left(\begin{array}{ccc}2&1&0\\ \\2&0&\frac{1}{2}\\\\-1&0&\frac{1}{2}\end{array}\right)[/tex]