Question

Помогите решить линейное уравнении методом Гаусса

Answer 1

$\left(\begin{array}{cccc}3&-1&2&\; |2\\4&-3&3&\; |3\\1&3&0&\; |0\\5&0&3&\; |3\end{array}\right)\sim \left(\begin{array}{cccc}1&3&0&\; |0\\0&-10&2&|2\\0&-15&3&\; |3\\0&-15&3&|3\end{array}\right)\sim \left(\begin{array}{cccc}1&3&0&\; |0\\0&-5&1&|1\end{array}\right)\\\\\\\left\{\begin{array}{ccc}x+3y=0\\-5y+z=1\end{array}\right\; \; \left\{\begin{array}{ccc}x+3y=0\\-5y=1-z\end{array}\right\; \; \left\{\begin{array}{ccc}x=-\frac{3(z-1)}{5}\\y=\frac{z-1}{5}\end{array}\right\\\\\\Otvet:\; \; \left\{\begin{array}{ccc}x=-\frac{3}{5}z+\frac{3}{5}\\y=\frac{1}{5}z-\frac{1}{5}\\z=z\end{array}\right\; .$