Question

Решите пример методом гаусса с действиями.

Answer 1

Составляем матрицу коэффициентов и преобразовываем ее:

$\left[\begin{array}{cccc}-4&1&-2&11\\5&2&-3&-28\\3&-4&1&-6\end{array}\right] = \left[\begin{array}{cccc}-4&1&-2&11\\0&3.25&-5.5&-14.25\\0&2.75&-0.5&-2.25\end{array}\right] = \left[\begin{array}{cccc}-4&1&-2&11\\0&3.25&-5.5&-14.25\\0&0&\frac{54}{13} &\frac{255}{26} \end{array}\right]$

$= \frac{54}{13}z =\frac{255}{26} = z = \frac{255}{108} = \frac{85}{36}\\3.25y - 5.5z = -14.25 = 325y - 550z = -1425 = 13y - 22z = -57 = 13y = 22 * \frac{85}{36} - 57 = \frac{935}{18} - 57 = -\frac{91}{18} = y = -\frac{91}{18}\\-4x + y - 2z = 11 = -4x = 11 + 2z - y = -4x = 11 + 2*\frac{85}{36} -(-\frac{91}{18}) = 11 + \frac{176}{18} = 11 + \frac{88}{9} = \frac{187}{9} = x = \frac{187}{36}\\ Answer: \\x = \frac{187}{36}\\y = -\frac{91}{18}\\z=\frac{85}{36}$