Question

resolva utilizando a regra de cramer
x+2y-z=-1
2x+y+z=4
x-y+5z=5

Answer 1

$x + 2y - z = -1$
$2x + y + z = 4$
$x - y + 5z = 5$

$\Delta = det \left[\begin{array}{ccc}1&2&-1\\2&1&1\\1&-1&5\end{array}\right]$
$\Delta=1*det\left[\begin{array}{cc}1&1\\-1&5\end{array}\right]-2*det\left[\begin{array}{cc}2&-1\\-1&5\end{array}\right]+1*det\left[\begin{array}{cc}2&-1\\1&1\end{array}\right]$
$\Delta=1*(5+1)-2*(10-1)+1*(2+1)$
$\Delta=1*6-2*9+1*3$
$\Delta=6-18+3$
$\Delta=-9$
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$\Delta x = det \left[\begin{array}{ccc}-1&2&-1\\4&1&1\\5&-1&5\end{array}\right]$
$\Delta x=(-1)*(5+1)-4*(10-1)+5*(2+1)$
$\Delta x=(-1)*6-4*9+5*3$
$\Delta x=-6-36+15$
$\Delta x=-27$

$\Delta y=det\left[\begin{array}{ccc}1&-1&-1\\2&4&1\\1&5&5\end{array}\right]$
$\Delta y=1*(20 - 5) - 2*(-5+5) + 1*(-1+4)$
$\Delta y=1*15 - 2*0 + 1*3 \\ \Delta y=15 - 0 + 3 \\ \Delta y = 18$

$\Delta z=det\left[\begin{array}{ccc}1&2&-1\\2&1&4\\1&-1&5\end{array}\right]$
$\Delta z=1*(5+4) - 2*(10-1) + 1*(8+1) \\ \Delta z = 1*9 - 2*9 + 1*9 \\ \Delta z=9(1-2+1) \\ \Delta z=9(0) \\ \Delta z = 0$
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$x=\Delta x/\Delta \\ x=(-27)/(-9) \\ x=3$

$y=\Delta y/\Delta \\ y=18/(-9) \\ y=-2$

$z=\Delta z/\Delta \\ z=0/(-9) \\ z=0$

$S=(3,-2,0)$