Question #206759

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

y-10z=-8

2x-6y=8

x+2z=7


1
Expert's answer
2021-06-14T19:00:18-0400

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


{y10z=82x6y=8x+2z=7.\begin{cases}y-10z=-8 \\ 2x-6y=8 \\ x+2z=7\end{cases}.


(0110826081027)\left(\begin{array}{ccc|c} 0 & 1 & -10 & -8\\ 2 & -6 & 0 & 8 \\ 1 & 0 & 2 & 7\end{array}\right) ~ (1027011082608)\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 2 & -6 & 0 & 8 \end{array}\right) ~ 2R1+R3\Big|-2R_1+R_3\Big| ~


(1027011080646)\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & -6 & -4 & -6 \end{array}\right) ~ 6R2+R3\Big|6R_2+R_3\Big| ~ (102701108006454)\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & 0 & -64 & -54 \end{array}\right) ~


164R3\Big|-\frac{1}{64}R_3\Big| ~ (10270110800127/32)\left(\begin{array}{ccc|c} 1 & 0 & 2 & 7 \\ 0 & 1 & -10 & -8\\ 0 & 0 & 1 & 27/32 \end{array}\right) ~ R12R3,R2+10R3\Big|R_1-2R_3,R_2+10R_3\Big| ~


(10085/160107/1600127/32).\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=8516, y=716, z=2732.x=\frac{85}{16}, \ y = \frac{7}{16}, \ z = \frac{27}{32}.

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