Explicație pas cu pas:
[tex]\left\{\begin{array}{c}3x-6y+3z=10 \\ 2x+y+4z=4 \\ x-y-z=2 \end{array}\right.[/tex]
→
[tex]d = \left|\begin{array}{ccc} + 3& - 6& + 3\\ + 2& + 1& + 4\\ + 1& - 1& - 1\end{array}\right| = - 36 [/tex]
→
[tex]d(x) = \left|\begin{array}{ccc} + 10& + 4& + 2\\ + 2& + 1& + 4\\ + 1& - 1& - 1\end{array}\right| = - 60[/tex]
[tex]d(y)=\left|\begin{array}{ccc} + 3& + 10& + 3\\ + 2& +4& + 4\\ + 1& + 2& - 1\end{array}\right| = 24[/tex]
[tex]d(z)=\left|\begin{array}{ccc} + 3& - 6& + 10\\ + 2& + 1& + 4\\ + 1& - 1& + 2\end{array}\right| = - 12[/tex]
→
[tex]x = \frac{d(x)}{d} = \frac{ - 60}{ - 36} = \frac{5}{3} \\ [/tex]
[tex]y = \frac{d(y)}{d} = \frac{24}{ - 36} = - \frac{2}{3} \\ [/tex]
[tex]z = \frac{d(z)}{d} = \frac{ - 12}{- 36} = \frac{1}{3} \\ [/tex]
