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Exercise:
Let V be a vector space over K and W subseteq V a subspace. Then W is a vector space on its own when owed with the operations from V.

Solution:
Proof. LSS closed under addition+LSS closed under multiplication Longrightarrow the operations + and from V induce operations on W. The fact that these operations on W satisfy the axioms of a vector space follows by direct verification.
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Exercise:
Let V be a vector space over K and W subseteq V a subspace. Then W is a vector space on its own when owed with the operations from V.

Solution:
Proof. LSS closed under addition+LSS closed under multiplication Longrightarrow the operations + and from V induce operations on W. The fact that these operations on W satisfy the axioms of a vector space follows by direct verification.
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eth, hs22, lineare algebra, proof, vector space
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(2, default)
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0 (default)
Language
ENG (English)
Type
Proof
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