Найти фундаментальную систему решений системы уравнения №3.1 во вложении
Система совместна и имеет ранг 2.Найдем фундаментальные решения принимая x3 и x4 за {1.0} и {0.1} соответственно:
![\left[\begin{array}{rrrr|r}1&5&4&3&1\\2&-1&2&-1&0\\5&3&8&1&1\end{array}\right]=\\= \left[\begin{array}{rrrr|r}1&5&4&3&1\\0&11&6&7&2\\0&22&12&14&4\end{array}\right]=\\=\left[\begin{array}{rrrr|r}1&5&4&3&1\\0&11&6&7&2\\0&0&0&0&0\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7Cr%7D1%265%264%263%261%5C%5C2%26-1%262%26-1%260%5C%5C5%263%268%261%261%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7Cr%7D1%265%264%263%261%5C%5C0%2611%266%267%262%5C%5C0%2622%2612%2614%264%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Brrrr%7Cr%7D1%265%264%263%261%5C%5C0%2611%266%267%262%5C%5C0%260%260%260%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{rrrr|r}1&5&4&3&1\\2&-1&2&-1&0\\5&3&8&1&1\end{array}\right]=\\= \left[\begin{array}{rrrr|r}1&5&4&3&1\\0&11&6&7&2\\0&22&12&14&4\end{array}\right]=\\=\left[\begin{array}{rrrr|r}1&5&4&3&1\\0&11&6&7&2\\0&0&0&0&0\end{array}\right]")
![\vec x_1= \left[\begin{array}{r}-\frac{13}{11}&-\frac{4}{11}&1&0\end{array}\right];\vec x_2= \left[\begin{array}{r}\frac{3}{11}&-\frac{5}{11}&0&1\end{array}\right];](https://tex.z-dn.net/?f=%5Cvec+x_1%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Br%7D-%5Cfrac%7B13%7D%7B11%7D%26-%5Cfrac%7B4%7D%7B11%7D%261%260%5Cend%7Barray%7D%5Cright%5D%3B%5Cvec+x_2%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Br%7D%5Cfrac%7B3%7D%7B11%7D%26-%5Cfrac%7B5%7D%7B11%7D%260%261%5Cend%7Barray%7D%5Cright%5D%3B "\vec x_1= \left[\begin{array}{r}-\frac{13}{11}&-\frac{4}{11}&1&0\end{array}\right];\vec x_2= \left[\begin{array}{r}\frac{3}{11}&-\frac{5}{11}&0&1\end{array}\right];")