- #1
Firepanda
- 430
- 0
If a problem I'm doing asks to find
V2 where V is a vector
is it simply the dot product of the vector, or the cross product?
The question: Which of the following sets of vectors v = {v1,...,vn} in Rn are subspaces of Rn (n>=3)
iii) All v such that V2=V12
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 = (a1,...,an) and b = (b1,...,bn)
then a+b = (a1+b1,...,an+bn)
and so (a+b)2=(a1+b1,...,an+bn)2=(a1+b1,...,an+bn).(a1+b1,...,an+bn)
= a12+2a1b1+b12+.. (dot product)
Which is a scalar field not a vector field, so it's not closed under addition.
Am I wrong?
V2 where V is a vector
is it simply the dot product of the vector, or the cross product?
The question: Which of the following sets of vectors v = {v1,...,vn} in Rn are subspaces of Rn (n>=3)
iii) All v such that V2=V12
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 = (a1,...,an) and b = (b1,...,bn)
then a+b = (a1+b1,...,an+bn)
and so (a+b)2=(a1+b1,...,an+bn)2=(a1+b1,...,an+bn).(a1+b1,...,an+bn)
= a12+2a1b1+b12+.. (dot product)
Which is a scalar field not a vector field, so it's not closed under addition.
Am I wrong?
Last edited: