Question

If W1 and W2 be two subspace of a vectors space V(F), Then (W1+W2)
(a) May not be a subspace
(b) will be a subspace
(c) may be a subspace
(d) none of these ​

Answer 1

Answer:

May be a subspace

Step-by-step explanation:

Brainliest plz

Answer 2

Answer :

b) will be a subspace

Explanation :

Please refer to the attachment .

Some important information :

Vector space :

(V , +) be an algebraic structure and (F , + , •) be a field , then V is called a vector space over the field F if the following conditions hold :

1. (V , +) is an abelian group .
2. ku ∈ V ∀ u ∈ V and k ∈ F
3. k(u + v) = ku + kv ∀ u , v ∈ V and k ∈ F .
4. (a + b)u = au + bu ∀ u ∈ V and a , b ∈ F .
5. (ab)u = a(bu) ∀ u ∈ V and a , b ∈ F .
6. 1u = u ∀ u ∈ V where 1 ∈ F is the unity .

♦ Elements of V are called vectors and the lements of F are called scalars .

♦ If V is a vector space over the field F then it is denoted by V(F) .

Subspace :

A non empty subset W of the vector space V(F) is said to be a subspace of V if it itself forms a vector space over the same field F .

Linear sum :

If W₁ and W₂ are two subspaces of the vector space V(F) , then the sum W₁ + W₂ = {w₁ + w₂ : w₁ ∈ W₁ , w₂ ∈ W₂} is called the linear sum of W₁ and W₂ .