- #1
Roni1985
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Homework Statement
Determine whether the following sets form subspaces of R^2 :
a) {(x1,x2)T | x1*x2=0}
b) {(x1,x2)T | x12=x22}
c) {(x1,x2)T | |x1|=|x2| }
Homework Equations
The Attempt at a Solution
My problem here is that I don't think I understand how the vectors look.
for instance,
{(x1,x2)T | x1*x2=0}
I say that each vectors looks like this:
[c,0]T
why zero ? because x2=0/x1
and x1=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.