Question

Gauss-Jordan

3x-2y+5z=38

2x+4y-z=-7

-7x-3y+4z=5

​

Answer 1

Aplicando el Método de Gauss Jordan para la solución del sistema de ecuaciones se obtiene:

x = 3

y = -2

z = 5

Explicación:

Dada;

Sistema de ecuación de 3x3;

3x-2y+5z=38

2x+4y-z=-7

-7x-3y+4z=5

El método de Gauss Jordan para el calculo de sistemas de ecuaciones;

Se debe formar: Mx = I

Siendo, I la matriz identidad;

M: $\left[\begin{array}{ccc}3&-2&5\\2&4&-1\\-7&-3&4\end{array}\right]$

x: $\left[\begin{array}{c}x&y&z\end{array}\right]$

I:$=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Construir Mx = I;

$\left[\begin{array}{ccc}3&-2&5\\2&4&-1\\-7&-3&4\end{array}\right]$·$\left[\begin{array}{c}38&-7&5\end{array}\right]$$=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

= $\left[\begin{array}{ccc}3&-2&5\\2&4&-1\\-7&-3&4\end{array}\right]$·$\left[\begin{array}{c}38&-7&5\end{array}\right]$

1/3f₁

f₂ -2/3f₁

f₃+7/3f₁

= $\left[\begin{array}{ccc}1&-2/3&5/3\\0&16/3&-13/3\\0&-23/3&47/3\end{array}\right]$·$\left[\begin{array}{c}38/3&-97/3&281/3\end{array}\right]$

3/16f₂

= $\left[\begin{array}{ccc}1&-2/3&5/3\\0&1&-13/16\\0&-23/3&47/3\end{array}\right]$·$\left[\begin{array}{c}38/3&-97/16&281/3\end{array}\right]$

f₃+23/3f₁

=  $\left[\begin{array}{ccc}1&-2/3&5/3\\0&1&-13/16\\0&0&151/16\end{array}\right]$·$\left[\begin{array}{c}38/3&-97/16&755/16\end{array}\right]$

16/151f₃

=  $\left[\begin{array}{ccc}1&-2/3&5/3\\0&1&-13/16\\0&0&1\end{array}\right]$·$\left[\begin{array}{c}38/3&-97/16&5\end{array}\right]$

f₁ - 5/3f₃

f₂ + 13/16f₃

=  $\left[\begin{array}{ccc}1&-2/3&0\\0&1&0\\0&0&1\end{array}\right]$·$\left[\begin{array}{c}13/3&-2&5\end{array}\right]$

f₁+ 2/3f₂

=  $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$·$\left[\begin{array}{c}3&-2&5\end{array}\right]$