Consider componentwise addition of element of rn and scalar

Question

1. Consider componentwise addition of element of Rⁿ, and scalar multiplication defind by c_x= {0 if c = 0 , x otherwise} for all c member of R and x meber meber of Rⁿ. With these definitions, is Rⁿ a vector space over R?

2. Conseder the sub space of P₄(R) given by S = { f (x) member of P₄ (R)| f (0)= f (1)=0} find a bais for S.