Question

resolva o sistema utilizando a regra de cramer [2x-y -4z=3 -x+3y+z=-10 3x+2y-2z=-2"

Answer 1

$2x-y-4z=3\\ -x+3y+z=-10\\ 3x+2y-2z=-2$

$\Delta = \left[\begin{array}{ccccc}2&-1&-4&2&-1\\-1&3&1&-1&3\\3&2&-2&3&2\end{array}\right] \\ \\ \Delta =-12-3+8+36-4+2\\ \Delta =-19+46\\ \Delta =27$


$\Delta x= \left[\begin{array}{ccccc}3&-1&-4&3&-1\\-10&3&1&-10&3\\-2&2&-2&-2&2\end{array}\right] \\ \\ \\ \Delta x=-18+2+80-24-6+20\\ \Delta x=102-48\\ \Delta x=54$


$\Delta y= \left[\begin{array}{ccccc}2&3&-4&2&3\\-1&-10&1&-1&-10\\3&-2&-2&3&-2\end{array}\right] \\ \\ \\ \Delta y=40+9-8-120+4-6\\ \Delta y=53-134\\ \Delta y=-81$


$\Delta z= \left[\begin{array}{ccccc}2&-1&3&2&-1\\-1&3&-10&-1&3\\3&2&-2&3&2\end{array}\right] \\ \\ \\ \Delta z=-12+30-6-27+40+2\\ \Delta z=72-45\\ \Delta z=27$


$x=\frac { \Delta x }{ \Delta } =\frac { 54 }{ 27 } =2\\ \\ y=\frac { \Delta y }{ \Delta } =\frac { -81 }{ 27 } =-3\\ \\ z=\frac { \Delta z }{ \Delta } =\frac { 27 }{ 27 } =1$



$S=\{ (2,-3,1)\}$