V is any vector space,where
are subspace of V.
Prove U is not a subspace of the vector space V.
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V is any vector space,
Prove U is not a subspace of the vector space V.
For example, let us consider two subspaces S & T of the vector space R3 where S = {(x,y,z) : y=0 , z=0} T = {(x,y,z) : x=0, z=0}
let a=(1,0,0) belongs to S & b=(0,1,0) belongs to T. But a+b does not belong to SUT
You can't prove this, It isn't true unless you have restrictions onand
. For example, if the vector space is
,
, and
then
which certainly is a subspace.
What is true is thatis a subspace if and only if one is a subspace of the other.
In order to prove this, you will have to make use of the fact, which isn't true unless one is NOT a subspace of the other, that there exist a vector u in