Annette Sabin

2022-01-05

determine whether W is a subspace of the vector space.
$W=\left\{f:f\left(0\right)=-1\right\},V=C\left[-1,1\right]$

sonorous9n

Expert

See the vector space and checked wheather zero function belongs or not , if yes then check other conditions for subspace.
$W=\left\{f:f\left(0\right)=-1\right\},V=C\left[-1,1\right]$
∵ if $f\in W⇒f\left(0\right)=-1$
and $0\left(0\right)=0$ [0 = zero function]
so $0\notin W$
so zero function does not belongs to W
so W is not subspace

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