1. ## Vector Spaces

Hey,

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

"The set of all first-degree polynomial functions $\displaystyle ax+b$, $\displaystyle a\neq0$, whose graphs pass through the origin with the standard operations"

By #4 "$\displaystyle V$ has a zero vector 0 such that for ever u in $\displaystyle V$, 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

2. 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 $\displaystyle ax+b$, $\displaystyle a\neq0$, whose graphs pass through the origin with the standard operations"

By #4 "$\displaystyle V$ has a zero vector 0 such that for ever u in $\displaystyle V$, 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 $\displaystyle \mathbf{0}\notin V$ (pay attention to the condition $\displaystyle a\neq0$ and the fact that each of them go through the origin, implying $\displaystyle b=0$). If we didn't have the condition $\displaystyle a\neq 0$, then it would be a vector space because the zero vector would exist.