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Linear Optimization (Math 423) Problem, prove an analog of the follow theorem: Thm 2.4: Consider the constraints...

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Advance Math

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

Thm 2.4: Consider the constraints Ax = b and x ? 0 andassume
that the m X n matrix A has linearly independent rows. Avector
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 AB(1),...,AB(m) are linearlyindependent;
(b} If i ? B(1),...,B(m), then xi = 0.

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