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erok81
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Homework Statement
Determine whether or not W is a subset of R4
W is the set of all vectors in R4 such that x1x2=x3x4
Homework Equations
Two methods.
u+v (addition)
cu (multiplication)
The Attempt at a Solution
I having trouble getting the hang of subspaces. I thought I was getting close to grasping it, until this problem.
u=(1,1,1,1) and v=(2,2,2,2) (is there a method to choosing these? I just chose points where the original statement still holds)
u+v=(3,3,3,3) which holds under addition.
cu=c(1,1,1,1) where c=2 (again, any method to this, or just choose something other than 0 or 1?)
=(2,2,2,2) which holds under multiplication.
Therefore it is a subspace. But...
The answer in the back states it is not a subspace, so I messed up somewhere. I think it has to do with choosing my u and v vectors.
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