Let $S$ denote $(x,y,z)\in \mathbb R^3$, which satisfies the inequalities: $$x - 2y + z \leq 1$$
$$2x + 2y - z \leq 5$$
$$-2x + y + z \leq 4$$
$$x \geq 1$$
$$y \geq 2$$
$$z \geq 3$$
How do I find the dimension of S?
I have tried to transform the inequalities into matrix form, but I'm not quite sure that this is even the right way.
