# Finding the dimension of S

## Homework Statement

Let S denote (x,y,z) in R3 which satisfies the following inequalities:
-2x+y+z <= 4
x-2y+z <= 1
2x+2y-z <= 5
x >=1
y >=2
z >= 3

## Homework Equations

How to find the dimension of the set S ?

## The Attempt at a Solution

I have tried to transform the inequalities into matrix form but I'm not quite sure that this is even the right way.

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## Homework Statement

Let S denote (x,y,z) in R3 which satisfies the following inequalities:
-2x+y+z <= 4
x-2y+z <= 1
2x+2y-z <= 5
x >=1
y >=2
z >= 3

## Homework Equations

How to find the dimension of the set S ?

## The Attempt at a Solution

I have tried to transform the inequalities into matrix form but I'm not quite sure that this is even the right way.

$$\begin{array}[rcccc] -2x+y+z&+s_1& & & =4 \\ x-2y+x & &+s_2& &=1 \\ 2x+2y-z & & &+s_3&=5\\ \end{array}\\ x \geq 1, y \geq 2, z \geq 3, s_1, s_2, s_3 \geq 0$$