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.
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!