Math Is Fun Forum

basmah

Member

Registered: 2006-10-02

Posts: 18

Proof help needed!!!

There are two proofs that i need help in:

Q#1) Prove that in a given vector space V, the zero vector is unique

and

Q#2) Let V and W be two subspaces of a vector space U. Prove that the set

V + W = {u : u = v + w, where v € V and w € W}

is a subspace of U.

V = {(x,0) : x is a real number} and W = {(0,y) : y is a real number}.

** Bold = Vector and "€" = "such that"

Last edited by basmah (2006-10-03 16:06:27)

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Proof help needed!!!

Suppose a zero vector is defined as such:
0+x=x

And suppose a=0 and b=0 at the same time.

then
a+b=a
a+b=b

thus a=b

For the second one, I forgot what makes a subspace. Maybe someone else could answer you.

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