Question

Does this set form a vector space?

Answer 1

I think the answer is No. But not sure

Answer 2

maybe bcz if you have 3*p(6) = 6 i.e. not in set

Answer 3

Exactly ! one contradiction is sufficient to end the proof

Answer 4

and also p(6) + p(6) = 4 i.e. not in set either. So it contradicts both additive and multiplication property

Answer 5

also, if u want to check another property that fails :

if p(t) and q(t) are in vector space, then the polynomial defined by p(t) + q(t) doesnt exist in this vector space because :
p(6) + q(6) = 2+2 = 4 \(\ne\) 2

Answer 6

thats what I said above, haha thank you

Answer 7

Ah ok, the replies are getting jumbled at my side