Vector Subspaces

• Dec 13th 2010, 07:18 AM
cassius
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
• Dec 13th 2010, 07:44 AM
Drexel28
Quote:

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?
• Dec 13th 2010, 07:53 AM
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...
• Dec 13th 2010, 07:54 AM
Drexel28
Quote:

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?
• Dec 13th 2010, 08:00 AM
cassius
Quote:

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