(a) Prove that a non-empty subset S of a vector space V over a field…
Previous year question for Engineering Mathematics-III.
Question
(a) Prove that a non-empty subset S of a vector space V over a field F is a subspace of V if and only if $\alpha x + \beta y \in S$ for all $\alpha, \beta \in F$ and $x, y \in S$.
(b) Let V be a vector space over a field F. Then prove the following :
(i) Any subset of V containing a zero element is linearly dependent.
(ii) Every subset of a linearly independent set of vectors is linearly independent.
- Year: 2022
- Subject: Engineering Mathematics-III