Question

S:3x-6y+3z=10
S:2x+y+4z=4
S:x-y-z=2

3x+4y+2z=11
-2y+3y+3z=1
2x-y+5z=-11
X+2y-6z=1
2x+3y+4z=8
-x+y+z=0
X+y+z=0

2x+y+3z=0
-x+4y-3z=-3.

Answer 1

Explicație pas cu pas:

$\left\{\begin{array}{c}3x-6y+3z=10 \\ 2x+y+4z=4 \\ x-y-z=2 \end{array}\right.$

→

$d = \left|\begin{array}{ccc} + 3& - 6& + 3\\ + 2& + 1& + 4\\ + 1& - 1& - 1\end{array}\right| = - 36$

→

$d(x) = \left|\begin{array}{ccc} + 10& + 4& + 2\\ + 2& + 1& + 4\\ + 1& - 1& - 1\end{array}\right| = - 60$

$d(y)=\left|\begin{array}{ccc} + 3& + 10& + 3\\ + 2& +4& + 4\\ + 1& + 2& - 1\end{array}\right| = 24$

$d(z)=\left|\begin{array}{ccc} + 3& - 6& + 10\\ + 2& + 1& + 4\\ + 1& - 1& + 2\end{array}\right| = - 12$

→

$x = \frac{d(x)}{d} = \frac{ - 60}{ - 36} = \frac{5}{3}$

$y = \frac{d(y)}{d} = \frac{24}{ - 36} = - \frac{2}{3}$

$z = \frac{d(z)}{d} = \frac{ - 12}{- 36} = \frac{1}{3}$