Let A x ≤ b be a system of linear inequalities where A ∈ R m × n , x ∈ R n and b ∈ R m Suppose A is a matrix with linearly independent rows.I wonder what would be the geometric or intuitive interpretations of these independent constraints?

Question

Let   A  x  ≤  b be a system of linear inequalities where   A  ∈      R          m      ×      n      ,   x  ∈      R    n   and   b  ∈      R    m  Suppose   A is a matrix with linearly independent rows.I wonder what would be the geometric or intuitive interpretations of these independent constraints?

Gloletheods6g · Accepted Answer

Normally, linear independence of the rows of   A is considered when the constraints are expressed as   A  x  =  b,   x  ≥  0, rather than as   A  x  ≤  b. In the equation constraints situation, you can eliminate linearly dependent rows of   A without changing the feasible set. You can&#039;t do that in the   A  x  ≤  b form.

aniawnua · Accepted Answer

This is kind of a long comment instead of answer. I think   A  x  ≤  b, with   A containing linearly independent rows will always be an unbounded set. While it&#039;s pretty straight forward to see geometrically. I am wondering if there exits a formal proof.

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