# Homework Help: System of linear inequalities

1. Apr 11, 2009

### saltine

1. The problem statement, all variables and given/known data

Determine whether a vector x exists that satisfies the above equation.

2. Relevant equations
This is not an actual HW problem, and it is not from a book. (There is no section before or after that explains or introduce this problem or problems similar to it.) So I don't know what topic this problem belongs to. I was wondering what the proper name of this type of problem is called, and what is the normal way (correct way) to solve it.

3. The attempt at a solution

At the moment all I could conclude is:

a > 0
b > 6a > 0
c > -11a + 6b > 26a > 0
d < 0, because:
-6b-110d +e > 0, since b>0 and e<0 (see below), therefore d must be negative.
d > 6a - 11b + 110c > 6a - 11b + 110(26a) = 2866a - 11b
e > 6b + 110d > 36a + 110(2866a - 11b) = 315296a - 1210b

Since e<0,

315296a - 1210b < 0
b > 261a

An now this screws up the inequality above, where I had "b > 6a".

I am stumped because I don't know how to combine the equations. Suppose it was not an inequality, so that I am just trying to find a vector such that the product is the zero-vector, then I could conclude that:

a = 0, therefore:
b = 0, therefore:
c = 0, therefore:
d = 0, therefore:
e = 0.

So the only solution for x is trivial. But does this result relate in some way to the inequality?

I was hoping that there is a proper way to view this problem, or that there is something method that would immediately tell whether the problem has a solution.

- Thanks