Question

regra de cramer : x=2y+z=1 2x+y- 3=0 x+3y-2z=-3
Me ajudaaa por favor

Answer 1

É só fazer:

$\begin{Bmatrix}x+2y+z&=&1\\2x+y-3&=&0\\x+3y-2z&=&-3\end{matrix}$

$D=\begin{vmatrix}1&2&1\\2&1&0\\1&3&-2\end{vmatrix}=11$

Agora

$D_x=\begin{vmatrix}1&2&1\\3&1&0\\-3&3&-2\end{vmatrix}=22$

$D_y=\begin{vmatrix}1&1&1\\2&3&0\\1&-3&-2\end{vmatrix}=-11$

$D_z=\begin{vmatrix}1&2&1\\2&1&3\\1&3&-3\end{vmatrix}=11$

Dai

$x=\frac{D_x}{D}=\frac{22}{11}=2$

$y=\frac{D_y}{D}=\frac{-11}{11}=-1$

$z=\frac{D_z}{D}=\frac{11}{11}=1$

$\therefore S=\{2,-1,1\}$