determine whether W is a subspace of the vector space. W

Annette Sabin 2022-01-05 Answered
determine whether W is a subspace of the vector space.
\(\displaystyle{W}={\left\lbrace{f}:{f{{\left({0}\right)}}}=-{1}\right\rbrace},{V}={C}{\left[-{1},{1}\right]}\)

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sonorous9n
Answered 2022-01-06 Author has 5052 answers
See the vector space and checked wheather zero function belongs or not , if yes then check other conditions for subspace.
\(\displaystyle{W}={\left\lbrace{f}:{f{{\left({0}\right)}}}=-{1}\right\rbrace},{V}={C}{\left[-{1},{1}\right]}\)
∵ if \(\displaystyle{f}\in{W}\Rightarrow{f{{\left({0}\right)}}}=-{1}\)
and \(\displaystyle{0}{\left({0}\right)}={0}\) [0 = zero function]
so \(\displaystyle{0}\notin{W}\)
so zero function does not belongs to W
so W is not subspace
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