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https://texercises.com/exercise/additional-characteristics-of-vector-spaces/
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Exercise:
abcliste abc The vector is unique. To avoid confusion e.g. with in K we will sometimes denote it by _V. abc The element v' corresponding to v is unique. We'll denote it by -v. We'll also write w-v : w+-v for all win V. abc forall vin V we have v i.e. _K v _V. abcliste

Solution:
abcliste abc Uniqueness of . Suppose ein V is an element that satisfy e+vv forall vin V. We'll prove e. Indeed e+ by asption. We now have e++ee abc Suppose v' und w both satisfy v+v' v+w leads to w+wv+v'+wv'+v+wv'+v+wv'++v'v' abc Let vin V. We have to prove that v. Indeed v+ v v+ v. Add - v to both sides of the last equality and we get v+- v v+ v+- v v. abcliste
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Exercise:
abcliste abc The vector is unique. To avoid confusion e.g. with in K we will sometimes denote it by _V. abc The element v' corresponding to v is unique. We'll denote it by -v. We'll also write w-v : w+-v for all win V. abc forall vin V we have v i.e. _K v _V. abcliste

Solution:
abcliste abc Uniqueness of . Suppose ein V is an element that satisfy e+vv forall vin V. We'll prove e. Indeed e+ by asption. We now have e++ee abc Suppose v' und w both satisfy v+v' v+w leads to w+wv+v'+wv'+v+wv'+v+wv'++v'v' abc Let vin V. We have to prove that v. Indeed v+ v v+ v. Add - v to both sides of the last equality and we get v+- v v+ v+- v v. abcliste
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eth, field, hs22, lineare algebra, proof, vector space
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ENG (English)
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Proof
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