Answer to Question #206759 in Linear Algebra for Johnny Banda

Question

Use GAUSS-JORDAN INVERSE METHOD to solve these system of Linear Equations.

y-10z=-8

2x-6y=8

x+2z=7

Answer 1

Let us use Gauss-Jordan method to solve the following system of linear equations:

$\begin{cases}y-10z=-8 \\ 2x-6y=8 \\ x+2z=7\end{cases}.$

$\left(\begin{array}{ccc|c} 0 & 1 & -10 & -8\\ 2 & -6 & 0 & 8 \\ 1 & 0 & 2 & 7\end{array}\right)$ ~ $\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 2 & -6 & 0 & 8 \end{array}\right)$ ~ $\Big|-2R_1+R_3\Big|$ ~

$\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & -6 & -4 & -6 \end{array}\right)$ ~ $\Big|6R_2+R_3\Big|$ ~ $\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & 0 & -64 & -54 \end{array}\right)$ ~

$\Big|-\frac{1}{64}R_3\Big|$ ~ $\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & 0 & 1 & 27/32 \end{array}\right)$ ~ $\Big|R_1-2R_3,R_2+10R_3\Big|$ ~

$\left(\begin{array}{ccc|c} 1 & 0 & 0 & 85/16 \\ 0 & 1 & 0& 7/16\\ 0 & 0 & 1 & 27/32 \end{array}\right).$

It follows that $x=\frac{85}{16}, \ y = \frac{7}{16}, \ z = \frac{27}{32}.$