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## Homework Statement

let

**V**be the vector space consisting of all infinite real sequences. Show that the subset

**W**consisting of all such sequences with only finitely many non-0 entities is a subspace of

**V**

## The Attempt at a Solution

Ok so i have to show 1.Closure under Addition,2. Closure under Scalar Multiplcation

let x=(x[tex]_{n}[/tex]),y=(y[tex]_{n}[/tex]) [tex]\in[/tex]

**W**

x + y [tex]\in[/tex]

**W**closed under addition and since

**W**is a set of finite sequences [tex]\in[/tex]

**V**as it consists of infinite sequences

[tex]\lambda[/tex] is a scalar and [tex]\lambda[/tex]x [tex]\in[/tex]

**W**closed under scalar multiplication and since

**W**is a set of finite sequences [tex]\in[/tex]

**V**as it consists of infinite sequences

I think this proves it

...But if [tex]\lambda[/tex] is negative this proof doesnt work,is there something i am missing or have i provided the required proof?

Thanks

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