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## Homework Statement

Prove that the set of all scalar multiples of the vector [1,3,2] in R3 forms a vector space with th usual operations on 3-vectors.

## Homework Equations

I am struggling to get anywhere on with this on paper. I know intuitively it and since its an intro course its a elementary problem, but am not getting to an actual proof. Of note: I am in transition to proofs in an undergraduate math degree...hence the struggle (I am reading some books on this as well).

## The Attempt at a Solution

I have decent/real written attempt here.

I assume that I need to prove scalar multiplication as well as addition are closed, and then of course the other eight properties. To do so would I just take

Scalar = k

k[1,2,3] = [k, 3k, 2k]

and any general vector in R3 [a,b,c] + [1,3,2] = [a + 1, b + 3, c + 3]

Then go on to the other properties....or am I way off? I feel like this is not even close to correct or sufficient, and obviously not formal enough.

Thanks in advance!