Question

Resolver o sistema linear utilizando a regra de Cramer:
{ x + 2y − z = 3
2x − y + 3z = 6
x + y − 2z = 1

Answer 1

Resposta:

(2,1,1)

Explicação passo a passo:

D=$\left[\begin{array}{ccc}1&2&1\\2&-1&3\\-1&1&-2\end{array}\right]$ $\left[\begin{array}{ccc}1&2\\2&-1\\1&1\end{array}\right]$ = 2+6-2-1-3+8=10

Dx=$\left[\begin{array}{ccc}3&2&-1\\6&-1&3\\1&1&-2\end{array}\right]$ $\left[\begin{array}{ccc}3&2\\6&-1\\1&1\end{array}\right]$ = 6+6-6-1-9+24=20

Dy=$\left[\begin{array}{ccc}1&3&-1\\2&6&3\\1&1&-2\end{array}\right]$ $\left[\begin{array}{ccc}1&3\\2&6\\1&1\end{array}\right]$ = -12+9-2+6-3+12=10

Dz=$\left[\begin{array}{ccc}1&2&3\\2&-1&6\\1&1&1\end{array}\right]$ $\left[\begin{array}{ccc}1&2\\2&-1\\1&1\end{array}\right]$ = -1+12+6+3-6-4=10

X=$\frac{Dx}{D}$= $\frac{20}{10}$=2     Y=$\frac{Dy}{D}$= $\frac{10}{10}$=1      Z=$\frac{Dz}{D}$= $\frac{10}{10}$=1              Obs: Sim sou do clóvis, quem é?