Question

Linear Optimization (Math 423) Problem, prove an analog of the follow theorem:

Thm 2.4: Consider the constraints Ax = b and x ≥ 0 and assume
that the m X n matrix A has linearly independent rows. A vector
x ∈ Rⁿ is a basic solution if and only if we have Ax = b, and there
exist indices B(1), ... , B(m) such that:
(a} The columns A_B(1),...,A_B(m) are linearly independent;
(b} If i ≠ B(1),...,B(m), then x_i = 0.

Answer 1