Hi,
Could someone explain to me why the set of all elements of R^3 with the first component of 1 is not a real vector space? I'm lost on this one. Thanks,
Kim
Consider vectors: $\displaystyle \bold{u} = (1, u_{2}, u_{3})$ and $\displaystyle \bold{v} = (1, v_{2}, v_{3})$.
One of the axioms state that if u and v are vectors in your vector space, then so should u + v. However:
$\displaystyle \bold{u} + \bold{v} = (2, u_{2} + v_{2}, u_{3} + v_{3}) $
which does not belong in your vector space.