Chan Pope
12/30/2023 · Primary School

Example \( 2, f \). The set consisting of only zero vector in a vector space \( V \) is a subspace of \( V \) That is, \( V_{D}=\left\{0_{\psi}\right\} \) is a subspace of \( V \), where \( 0_{V} \) is the zero vector in \( V, V_{0} \) is the smallest subspace of \( V \), called zero subspace of \( V \).

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The set containing only the zero vector, \( V_0 = \{ 0_V \} \), is a subspace of \( V \) because it is non-empty, closed under addition, and closed under scalar multiplication. It is called the zero subspace of \( V \) and is the smallest subspace.

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