1. ## Vector Subspaces

Are the following vector subspaces??
$\displaystyle X= (x \in Q^4: x_1+x_2-x_3-x_4=x_1+x_4=0)$

and

$\displaystyle X=(x\in Q^4: x_1^2+x_2^2-x_3^2-x_4^2=0)$

I don't think the second one is (under addition x+y) but i'm not sure

2. Originally Posted by cassius
Are the following vector subspaces??
$\displaystyle X= (x \in Q^4: x_1+x_2-x_3-x_4=x_1+x_4=0)$

and

$\displaystyle X=(x\in Q^4: x_1^2+x_2^2-x_3^2-x_4^2=0)$

I don't think the second one is (under addition x+y) but i'm not sure
Why do you think so? Let's see some reasoning?

3. hi!
I thought if we take $\displaystyle Y\in Q^4...$ then $\displaystyle (x_1+y_1)^2$is not the same as $\displaystyle x_1^2+y_1^2$ etc...

4. Originally Posted by cassius
hi!
I thought if we take $\displaystyle Y\in Q^4...$ then $\displaystyle (x_1+y_1)^2$is not the same as $\displaystyle x_1^2+y_1^2$ etc...
Hmm, I'm not quite sure what you mean by this?

5. Originally Posted by Drexel28
Hmm, I'm not quite sure what you mean by this?
i'm sorry my friend confused me with this, she might have had transformations in mind

I know that for a subspace, if x and y are in the subspace then so is x+y
" " " x multiplied by scalar
" " " zero element