Question

Resolva o sistema de três equações aplicando a regra de Cramer :

( vou deixar aqui a resposta certa caso vocês precisem, me agradeçam depois ) ❤️

Answer 1

{ x - 2y + z = 1

{ 2x + y - z = 0

{ -x + 3y - 2z = -3

$\sf D=\left[\begin{array}{ccc}1&-2&1\\2&1&-1\\-1&3&-2\end{array}\right] \left[\begin{array}{ccc}1&-2\\2&1\\-1&3\end{array}\right]$

1*1*(-2) + (-2)*(-1)*(-1) + 1*2*3 - ( (-1)*1*1 + 3*(-1)*1 + (-2)*2*(-2) ) =

-2 + (-2) + 6 - (-1) - (-3) - 8 =

2 - 4 =

$\underline{\boxed{\red{\sf D=-2 }}}$

$\sf Dx=\left[\begin{array}{ccc}1&-2&1\\0&1&-1\\-3&3&-2\end{array}\right] \left[\begin{array}{ccc}1&-2\\0&1\\-3&3\end{array}\right]$

1*1*(-2) + (-2)*(-1)*(-3) + 1*0*3 - ( (-3)*1*1 + 3*(-1)*1 + (-2)*0*(-2) ) =

-2 + (-6) + 0 - (-3) - (-3) - 0 =

-8 + 6 =

$\underline{\boxed{\red{\sf Dx=-2 }}}$

$\sf Dy=\left[\begin{array}{ccc}1&1&1\\2&0&-1\\-1&-3&-2\end{array}\right] \left[\begin{array}{ccc}1&1\\2&0\\-1&-3\end{array}\right]$

1*0*(-2) + 1*(-1)*(-1) + 1*2*(-3) - ( (-1)*0*1 + (-3)*(-1)*1 + (-2)*2*1 ) =

0 + 1 + (-6) - 0 - 3 - (-4) =

- 5 + 1 =

$\underline{\boxed{\red{\sf Dy= -4 }}}$

$\sf Dz=\left[\begin{array}{ccc}1&-2&1\\2&1&0\\-1&3&-3\end{array}\right] \left[\begin{array}{ccc}1&-2\\2&1\\-1&3\end{array}\right]$

1*1*(-3) + (-2)*0*(-1) + 1*2*3 - ( (-1)*1*1 + 3*0*1 + (-3)*2*(-2) ) =

-3 + 0 + 6 - (-1) - 0 - 12 =

3 - 11 =

$\underline{\boxed{\red{\sf Dz= -8}}}$

$\left[\begin{array}{ccc}\sf x= \dfrac{Dx}{D}\ ;\ y= \dfrac{Dy}{D}\ ;\ z=\dfrac{Dz}{D} \end{array}\right]$

$\left(\begin{array}{lr}\sf x= \dfrac{Dx}{D}= \dfrac{-2}{-2} \rightarrow x=\underline{\boxed{\red{\sf 1}}}\\\\\sf y= \dfrac{Dy}{D}=\dfrac{-4}{-2} \rightarrow y=\underline{\boxed{\red{\sf 2}}}\\\\\sf z=\dfrac{Dz}{D}=\dfrac{-8}{-2} \rightarrow z=\underline{\boxed{\red{\sf 4}}} \end{array}\right)$

Portanto: V = { ( 1 ; 2 ; 4 ) }

Podemos conferir se quisermos, veja:

{ x - 2y + z = 1

{ 2x + y - z = 0

{ -x + 3y - 2z = -3

x = 1

y = 2

z = 4

{ 1 - 2(2) + 4 = 1

{ 2(1) + 2 - 4 = 0

{ -1 + 3(2) - 2(4) = -3

Espero ter ajudado.

Bons estudos.

• Att. FireClassis.