Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space. 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 upper triangular 2 ✕ 2 matrices, with the usual matrix addition and scalar multiplicationAll of the axioms hold, so the given set is a vector space.1. u + v is in V.2. u + v = v + u3. (u + v) + w = u + (v + w)4. There exists an element 0 in V, called a zero vector, such that u + 0 = u.5. For each u in V, there is an element −u in V such that u + (−u) = 0.6. cu is in V.7. c(u + v) = cu + cv8. (c + d)u = cu + du9. c(du) = (cd)u10. 1u = u

Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space. 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 x y in ℝ2 with xy ≥ 0 (i.e., the union of the first and third quadrants), with the usual vector addition and scalar multiplication

Let V=Rn be a vector space and W = {(a1, a2,…, an) such that a2=a12. Check whether W isa subspace of V or not, with respect to usual addition and scalar multiplication.

Berapa jumlah aksioma yang harus dipenuhi agar suatu himpunan beserta operasinya dikatakan sebagai ruang vektor?How many axioms must be satisfied for a set along with its operations to be considered a vector space?A5B8C10D12

Say whether the following sets are vector subspaces of the vector space V in each of the following cases: 1) S1 = {(x, y) ∈ R 2 : |x| = |y|} , V = R 2

Manakah dari berikut ini yang merupakan aksioma distribusi dari perkalian skalar terhadap penjumlahan vektor dalam ruang vektor?Which of the following is the distributive axiom of scalar multiplication over vector addition in vector spaces?A𝑎(𝑢⃗+𝑣⃗)=𝑎𝑢⃗+𝑎𝑣⃗B𝑎(𝑢⃗⋅𝑣⃗)=(𝑎𝑢⃗)⋅𝑣⃗C𝑎𝑢⃗+𝑏𝑣⃗=(𝑎+𝑏)(𝑢⃗+𝑣⃗)D𝑎𝑢⃗⋅𝑣⃗=𝑎(𝑢⃗⋅𝑣⃗)