Graph the solution set of the system of inequalities. x-y<=2x-y<=2 x>=3

aflacatn 2020-10-21 Answered
Graph the solution set of the system of inequalities.
xy2xy2
x3
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Delorenzoz
Answered 2020-10-22 Author has 91 answers

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Let's say that we have a system of linear inequalities:
[ c 1 , 1 c 1 , 2 c 1 , n c 2 , 1 c 2 , 2 c 2 , n c m , 1 c m , 2 c m , n ] × [ x 1 x 2 x n ] [ b 1 b 2 b m ]
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Given the system
x = A x
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In what interval of a is the system asymptotically stable, and for what value of a is the system stable/unstable if such a case even exists?
Attempt
For a system to be asymptotically stable the real part of all eigenvalues must be negative.
( λ ) < 0 , for all λ
Since we are dealing with a 3 × 3 matrix, I used maple to find the eigenvalues from the system matrix. I also tried to use Maple to solve the inequality case for the eigenvalues, but I don't think I'm getting correct results.
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Let A and B represent two linear inequalities:
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B : b 1 x 1 + . . . + b n x n k 2
If A and B is unsatisfiable (does not have solution), does the following hold in general (the conjunction of two inequalities implies the summation of them )? If so, I am looking for a formal proof?
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𝑎 1 𝑥 1 + . . . + 𝑎 n 𝑥 n 𝑘 1 𝑏 1 𝑥 1 + . . . 𝑏 n 𝑥 n 𝑘 2 𝑎 1 𝑥 1 + . . . + 𝑎 n 𝑥 n + 𝑏 1 𝑥 1 + . . . 𝑏 n 𝑥 n 𝑘 1 + 𝑘 2
and then I would like to generalize the above theorem to summation of several inequalities.