Question

S is a non-empty subset of vector space V, then the smallest subspace of V containing

S is....

(a) s
(b) {s}

(c) [S]
(d) None​

Answer 1

Answer:

option c, I think so not sure

Answer 2

Concept:

We first recall the concept of subspace of a vector space to answer this question.

A non empty subset W of a vector space V over a field F, V(F) ,is called a subspace of V(F) if and only if W is a vector space itself over F with respect to same composition vector addition and scalar multiplication.

Given:

S is a non empty subset of vector space V

To find:

The smallest subspace of V containing S

Solution:

The set of all linear combination of vector of a non empty subset S of V define span(S) also denoted by [S}

Span (S) is the smallest subspace of V

Hence, the smallest subspace of V containing S is [S].

option (c) is the correct choice.