How to check if the inequality Ax<b admits at least one solution. Entries of A, x and b are taken in Z

Yazmin Sims

Yazmin Sims

Answered question

2022-10-24

How to check if the inequality A x < b admits at least one solution. Entries of A, x and b are taken in Z

Answer & Explanation

Liam Everett

Liam Everett

Beginner2022-10-25Added 16 answers

First assume A,b>0; in this case by taking any integer x<0 you are done.
Now assume A<0 and b>0; in this case by taking any integer x>0 you are done again.
Now assume A>0 and b<0; in this case by taking x=b you are done.
Finally, assume A<0 and b<0; in this case by taking x=−b you are done.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?