Linear Algebra Is the following set V vector space? Prove or give a counter example. V = {a_n} | n ∈ N, a_n ∈ R , that is, V is the set of sequences {a_n} of real numbers, with vector addition and...

Linear Algebra

Is the following set V vector space? Prove or give a counter example.

V = {a_n} | n ∈ N, a_n ∈ R , that is, V is the set of sequences {a_n} of real numbers, with vector addition and scalar multiplication defined by

{a_n} + {b_n} = {a_n + b_n},

t{a_n} = {ta_n}, t ∈ R.

where R is the set of real numbers.