Thread: Vector Spaces

Hey,

I am having trouble seeing why the following is not a vector space.

"The set of all first-degree polynomial functions , , whose graphs pass through the origin with the standard operations"

By #4 " has a zero vector 0 such that for ever u in , u+0=u"

I am not seeing why #4 keeps the above from being a vector space. I don't think I am understanding the zero vector as I should.

Thanks

Originally Posted by Danneedshelp

Hey,

I am having trouble seeing why the following is not a vector space.

"The set of all first-degree polynomial functions , , whose graphs pass through the origin with the standard operations"

By #4 " has a zero vector 0 such that for ever u in , u+0=u"

I am not seeing why #4 keeps the above from being a vector space. I don't think I am understanding the zero vector as I should.

Thanks

#4 fails because (pay attention to the condition and the fact that each of them go through the origin, implying ). If we didn't have the condition , then it would be a vector space because the zero vector would exist.