(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

U={(x1,x2,x3)[itex]\in[/itex]ℝ3 | x1+x2=0}

Is this a linear subspace of ℝ3?

2. Relevant equations

x1+x2=0

3. The attempt at a solution

I know that in order to be a linear subspace, it must be closed under addition and scalar multiplication. I'm just not really sure how to incorporate the x1+x2=0. This is what I've done:

x=(x1,x2,x3), y=(y1,y2,y3)

x+y=(x1,x2,x3)+(y1,y2,y3)=(x1+y1, x2+y2, x3+y3)

but how does this relate to x1+x2=0? there is no "x1+x2" to check... Confused please help!

Edit:

Do I simply just show this?

(x1+y1)+(x2+y2)=

(x1+x2)+(y1+y2)=0+0=0 (closed under addition)

cx=c(x1,x2,x3)=(cx1,cx2,cx3)

(cx1+cx2)=

c(x1+x2)=c(0)=0 (closed under scalar multiplication)

So it is a subspace?

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# Determining if vectors in R3 are linear subspaces

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