Linear Algebra Doubts

[The Villain]

Which one of these are subspaces over R3..?

1.Let W-{(a1,a2,1 :a1,a2 belongs to R}

2.Let W={a(1,1,1) : a belongs to R}={(a,a,a) :a belongs to R}

3..Let W-{(a1,a2) :a1+a2=1,a1,a2 belongs to R}.Is it a subspace over R2.


Please explain the answers .Thanks

[kangkan]

which subject is tis?

[Arushi :))]

[Homer Simpson]

3 is not a subspace over R2

[The Villain]

Thanxx Arushi

But i didnt get 3...how is alpha equal to 2 for beta equal to1...

[Homer Simpson]

Ron, it suffices to show that (0.5,0.5) + (0.2,0.8) = (0.7,1.3) is not closed under addition.

(0.5,0.5) and (0.2,0.8) both belong to W
but their sum (0.7,1.3) doesn't belong to W as 0.7+1.3 = 2 (not equal to 1)