This exercise serves for improving the verbalization process. Consider the following system of inequalities

and x1 ≥ 0, x2 ≥ 0.
For the above system of inequalities, give the formal definition of

a) a basis

b) a feasible basis.
(Do not use the idea of a ruler, of a reference system, of a scaffolding and of a system of measurement units. These intuitive ideas served for introducing the notion of a basis. From now on we need the formal definition.)

c) Explain the meaning of linear independence between two vectors.

d) Characterize (describe) a basic feasible solution.

e) Using the input space, explain the geometric meaning of solving a system of linear equations.

a111a122 b 0211 0222 b2