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

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- Dec 13th 2010, 07:18 AMcassiusVector 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 AMDrexel28
- Dec 13th 2010, 07:53 AMcassius
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 AMDrexel28
- Dec 13th 2010, 08:00 AMcassius