Question: $$\text{Maximize } z=2x_1-6x_2$$
Subject to,
$$-x_1-x_2-x_3\le-2$$ $$2x_1-x_2+x_3\le1$$ $$x_1,x_2,x_3\ge0$$
My work:
$-2x_1+6x_2+z=0$
Then,
${R2\over2}\Rightarrow R2_{new}$,
$R2_{new} + R1\Rightarrow R1_{new}$,
$2\cdot R2_{new}+ R3\Rightarrow R3_{new}$.
The new matrix:
The last row has no negative value, and it looks like the job is done, but the answer is wrong. I think the mistake should be made on calculating, but I can't figure it out... Help!