- #1
depre87
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Homework Statement
Show if V is a vector space ([a,b,c]|ab>=0). I'm trying to test whether it is closed under
vector addition.
Homework Equations
v=[a1,b1,c1] w=[a2,b2,c2], v and w satisfy ab>=0
a1b1>=0, a2b2>=0
show (a1+a2)(b1+b2)>=0
The Attempt at a Solution
Got to a1b1 + a2b2 +a1b2 + a2b1 after expanding the above equation. Know a1b1 and a2b2 both >=0 however what do I do with the a1b2 and a2b1? I've attempted trying to factor them into a1b1 and have gotten a1b1[(b2/b1)+(a2/a1)] and know a1b1 >=0 however not sure what to do with the terms in the bracket to further prove whether or not it is closed under vector addition.