Determine whether the given set, together with the specified operations of addit

Question

Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space over the indicated Z_P. If it is not, select all of the axioms that fail to hold. (Let u, v, and w be vectors in the vector space V, and let c and d be scalars.) The set of all vectors in Z_2^n with an odd number of 1s, over Z_2 with the usual vector addition and scalar multiplication. All of the axioms hold, so the given set is a vector space. u + v is in V. u + v = v + u (u + v) + w = u + (v + w) There exists an element 0 in V, called zero vector, such that u + 0 = u. For each u in v, there is an element -u in V such that u + (-u) = 0. cu is in V. c(u + v) = cu + cv (c + d)u = cu + du c(du) = (cd)u 1u = u

Explanation / Answer

Yes this is a vector space over z2

All conditions are satisfied

As Z2n contains Z2

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