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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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