renegade05
Full Member
- Joined
- Sep 10, 2010
- Messages
- 260
\(\displaystyle s=\begin{Bmatrix}\vec{p}\in R^3 \mid \vec{p}\cdot[2,1,-3]=0 \mathrm{\ or\ } \vec{p}\cdot[5,-1,2]=0 \end{Bmatrix}\)
(a) Prove that S is closed under scalar multiplication.
(b) Prove that S is not closed under vector addition.
Alright, well I'm kinda drawing a blank on this one.
For (a) I am thinking i can go around it by doing something like showing if i take a scalar K and times it by either \(\displaystyle \vec{p}\) or the vectors it will still equal zero. I don't really know how to show this algebraically though.
And as for (b) I'm completely lost, how can i start this proof? Maybe with a counter example?
Please help.:cool:
(a) Prove that S is closed under scalar multiplication.
(b) Prove that S is not closed under vector addition.
Alright, well I'm kinda drawing a blank on this one.
For (a) I am thinking i can go around it by doing something like showing if i take a scalar K and times it by either \(\displaystyle \vec{p}\) or the vectors it will still equal zero. I don't really know how to show this algebraically though.
And as for (b) I'm completely lost, how can i start this proof? Maybe with a counter example?
Please help.:cool: