Hello,

I need help in this linear Algebra problem...

Prove that W1 = {(a1, a2, a3....a3)EF^n: a1+a2+a3+...+an = 0} is a subspace of F^n, but

W2 = {(a1, a2, a3....a3)EF^n: a1+a2+a3+...+an = 0} is not...

Thanks for the help in advance!

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- January 30th 2009, 09:37 PMVedicmathsLinear Algebra: Vector Space!
Hello,

I need help in this linear Algebra problem...

Prove that W1 = {(a1, a2, a3....a3)**E**F^n: a1+a2+a3+...+an = 0} is a subspace of F^n, but

W2 = {(a1, a2, a3....a3)**E**F^n: a1+a2+a3+...+an = 0} is not...

Thanks for the help in advance! - January 31st 2009, 11:48 AMclic-clac
What is written leads to , perhaps we should replace by in the definition of . If so, since a subspace of a vector space must contain and that we can conclude that doesn't contain and isn't a vector space.

By the way, contains So the only thing we have to prove now is that for every (if is a -vector space),

Let and be two elements of since

Therefore , and is a subspace of