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## Homework Statement

Determine whether the following sets form subspaces of R^2 :

a) {(x

_{1},x

_{2})

^{T}| x

_{1}*x

_{2}=0}

b) {(x

_{1},x

_{2})

^{T}| x

_{1}

^{2}=x

_{2}

^{2}}

c) {(x

_{1},x

_{2})

^{T}| |x

_{1}|=|x

_{2}| }

## Homework Equations

## The Attempt at a Solution

My problem here is that I don't think I understand how the vectors look.

for instance,

{(x

_{1},x

_{2})

^{T}| x

_{1}*x

_{2}=0}

I say that each vectors looks like this:

[c,0]

^{T}

why zero ? because x

_{2}=0/x

_{1}

and x

_{1}=c.

Now, if this is correct, it must be a subspace. because we can multiply by a constant and still be in the subspace, or add two vectors and be in the subspace. But, its not a subspace according to the answers.

The problem with the other two is that I don't even know how the vectors in the subspaces look.

Would appreciate any help.

Thanks,

Roni.