Question

Hola, podrían mandarme dos ecuaciones resueltas utilizando el método Cramer porfas

Answer 1

Hola!

Respuesta:

1.  $\left\{\begin{matrix} 2x-y+z=3 \\ 2y - z=1 \\ x-y=1 \end{matrix}\right.$

• Calculamos el determinante de la matriz de coeficientes_:

           ${\Delta= \left| \begin{array}{rrr} 2 & -1 & 1 \\ 0 & 2 & -1 \\ 1 & -1 & 0 \end{array} \right| = -3}$

• Calculamos los coeficientes

           ${x = \displaystyle \frac{\left| \begin{array}{rrr} 3 & -1 & 1 \\ 1 & 2 & -1 \\ 1 & -1 & 0 \end{array} \right|}{\Delta} = \frac{-5}{-3}=\frac{5}{3}}$

           ${y = \displaystyle \frac{\left| \begin{array}{rrr} 2 & 3 & 1 \\ 0 & 1 & -1 \\ 1 & 1 & 0 \end{array} \right|}{\Delta} = \frac{-2}{-3}=\frac{2}{3}}$

          ${z = \displaystyle \frac{\left| \begin{array}{rrr} 2 & -1 & 3 \\ 0 & 2 & 1 \\ 1 & -1 & 1 \end{array} \right|}{\Delta} = \frac{-1}{-3}=\frac{1}{3}}$

2. $\left\{\begin{matrix} x+y+z=1 \\ x-2y + 3z=2 \\ x+z=5 \end{matrix}\right.$

${\Delta= \left| \begin{array}{rrr} 1 & 1 & 1 \\ 1 & -2 & 3 \\ 1 & 0& 1 \end{array} \right| = 2}$           ${\Delta_{1} = \left| \begin{array}{rrr} 1 & 1 & 1 \\ 2 & -2 & 3 \\ 5 & 0 & 1 \end{array} \right| = 21}$

${\Delta_{2} = \left| \begin{array}{rrr} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 5 & 1 \end{array} \right| = -8}$         ${\Delta_{2} = \left| \begin{array}{rrr} 1 & 1 & 1 \\ 1 & -2 & 2 \\ 1 & 0 & 5 \end{array} \right| = -11}$

   $x=\dfrac{21}{2}$       $x=\dfrac{-8}{2}=-4$       $z=\dfrac{-11}{2}$

                                                                         Saludos!