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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...?