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I couldn't show this problem. Can somebody help me by this question?

Consider a polyhedron $\{X \in \mathbb{R}^n | AX \leq b, X \geq 0 \}$ and a non-degenerate basic feasible solution $X^*$. We introduce slack variables z and construct a corresponding polyhedron $\{(X,Z)| Ax + Z = b, X\geq 0, Z \geq 0\}$ in standard form. Show that $(X^*, b – AX^*)$ is a non-degenerate basic feasible solution for the new polyhedron.

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