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evinda

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The following system of restrictions is given:$$x_1+ 2 x_2 \leq 4 \\ 2x_1+x_2 \leq 2 \\ x_1+a x_2 \leq 3 \\ x_1, x_2 \geq 0$$

For which values of $a$ is there a degenarate basic feasible solution?

I wrote the above system of restrictions in canonical form as follows:$$x_1+ 2 x_2 +x_3= 4 \\ 2x_1+x_2 +x_4= 2 \\ x_1+a x_2 + x_5= 3 \\ x_1, x_2 , x_3, x_4, x_5\geq 0$$$$A=\begin{bmatrix}

1 & 2 & 1 & 0 & 0\\

2 & 1 & 0 & 1 & 0\\

1 & a & 0 & 0 & 1

\end{bmatrix}$$

The order of $A$ is $3$.I thought that for example for $x_1=x_2=0$ we get the non-degenerate basic feasible solution $(0,0,4,2,3)$.

Do we have to find an other non-degenerate basic feasible solution with a common component as the above one so that their subtraction gives a degenerate basic feasible solution? (Thinking)

How can we find an appropriate $a$? (Thinking)