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If a problem I'm doing asks to find

V

is it simply the dot product of the vector, or the cross product?

iii) All v such that V

He proved it by saying it's not closed under addition (axiom of a subspace)

By (1,1,0) + (-1,1,0) = (0,2,0)

And that concludes his proof, but I'm not seeing what he's proved there at all.

Personally I would have done let a = (a

then a+b = (a

and so (a+b)

= a

Which is a scalar field not a vector field, so it's not closed under addition.

Am I wrong?

V

^{2}where V is a vectoris it simply the dot product of the vector, or the cross product?

**The question: Which of the following sets of vectors v = {v**_{1},...,v_{n}} in R^{n}are subspaces of R^{n}(n>=3)iii) All v such that V

_{2}=V_{1}^{2}He proved it by saying it's not closed under addition (axiom of a subspace)

By (1,1,0) + (-1,1,0) = (0,2,0)

And that concludes his proof, but I'm not seeing what he's proved there at all.

Personally I would have done let a = (a

_{1},...,a_{n}) and b = (b_{1},...,b_{n})then a+b = (a

_{1}+b_{1},....,a_{n}+b_{n})and so (a+b)

^{2}=(a_{1}+b_{1},....,a_{n}+b_{n})^{2}=(a_{1}+b_{1},....,a_{n}+b_{n}).(a_{1}+b_{1},....,a_{n}+b_{n})= a

_{1}^{2}+2a_{1}b_{1}+b_{1}^{2}+.. (dot product)Which is a scalar field not a vector field, so it's not closed under addition.

Am I wrong?

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