Question

A non empty subset U of a vector space v(F) is a subspace of V iff​

Answer 1

Answer:

A subset W of a vector space V is a subspace if (1) W is non-empty (2) For every ¯v, ¯w ∈ W and a, b ∈ F, a¯v + b ¯w ∈ W. ... So a non-empty subset of V is a subspace if it is closed under linear combinations...

Step-by-step explanation:

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Answer 2

A non empty subset U of a vector space v(F) is a subspace of V :

Explanation:

• A vector space is a non-empty set V , whose elements are called vectors, on which there are defined two operations.
• addition, which to any two vectors v, w assigns a vector v + w, called the sum of v and w.
• addition is associative, i.e. (u + v) + w = u + (v + w) for any vectors u, v, w.
• So a non-empty subset of V is a subspace if it is closed under linear combinations.