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Homework Statement
Let V = V1 + V2, where V1 and V2 are vector spaces. Define M ={(x1, 0vector2): x1 in V1}
and N = {(0vector1, x2) : x2 in V2
0vector 1 is the 0v of V1 and 0vector is the 0v of V2 and 0v is 0 vector of V
a) prove hat both M and N are subspace of V
b) show that M n N = {0v}
c) show that M+N=V
Homework Equations
The Attempt at a Solution
I am not clear about what M intersection N is
is it that the intersection of M and N is the 0 vector? If so what are the first steps to show this?
as for a)
do uprove using cx1 + x2, where Yi = (Yi, 0v2) Yj = (Yj,0v2)
and so on...?