# Thread: Finding certain scalars to get a certain inequality?

1. ## Finding certain scalars to get a certain inequality?

So i am totally off the wall confused, with this:

-y1 - y2 - y3 <= -1 (1)
y1 - y2 + 5y3 <= 0 (2)
y1 + 2y2 - y3 <= 1 (3)

Then the question is:

Find nonengative scalars d1, d2, d3 such that d1 x (1) + d2 x (2) + d3 x (3) gives the inequality 0<=-1.

I don't understand... and i am getting really frusturated because we never did anything like this yet again in class.

Any suggestions?

2. Originally Posted by uberjumper
So i am totally off the wall confused, with this:

-y1 - y2 - y3 <= -1 (1)
y1 - y2 + 5y3 <= 0 (2)
y1 + 2y2 - y3 <= 1 (3)

Then the question is:

Find nonengative scalars d1, d2, d3 such that d1 x (1) + d2 x (2) + d3 x (3) gives the inequality 0<=-1.

I don't understand... and i am getting really frusturated because we never did anything like this yet again in class.

Any suggestions?
This is just like solving equations by succesive elimination. For example, I see that adding (1) and (2), I eliminate y1: (1)+ (2) gives -2y2+ 4y3.
Also adding (1) and (3) elimininates y1: (1)+ (3) gives y2- 2y3. Now I see that if I add the first of those to 2 times the second everything cancels! That is ((1)+ (2))+ 2((1)+ (3))= 3(1)+ (2)+ 2(3)= 0.

(No, I am not claiming 3+ 2+ 6= 5 . (1), (2), and (3) refer, of course, to the three inequalities.)

What do you get doing the same to the right side?