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https://texercises.com/exercise/criterion-linear-subspace/
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Exercise:
Let V be a vector space over K and W subseteq V a subset. Then W is a linear subspace of V iff the following holds. abcliste abc _V in W abc forall a_a_ in K w_w_ in W we have a_w_+a_w_in W abcliste

Solution:
Proof. W subseteq V is a subspace Longrightarrow + follow immediately from the fact that W is a vector space. +Longrightarrow W subseteq V is a linear subspace. Let w_w_ in W. By w_+ w_ in W. Let a in K win W. By a w+ w in W.
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Exercise:
Let V be a vector space over K and W subseteq V a subset. Then W is a linear subspace of V iff the following holds. abcliste abc _V in W abc forall a_a_ in K w_w_ in W we have a_w_+a_w_in W abcliste

Solution:
Proof. W subseteq V is a subspace Longrightarrow + follow immediately from the fact that W is a vector space. +Longrightarrow W subseteq V is a linear subspace. Let w_w_ in W. By w_+ w_ in W. Let a in K win W. By a w+ w in W.
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eth, hs22, lineare algebra, proof, vector space
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ENG (English)
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