Exercise
https://texercises.com/exercise/additional-characteristics-of-vector-spaces/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
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
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
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
Contained in these collections

Similar exercises (47)
Title Creator Matched on
Linear subspaces rk tags
Criterion linear subspace rk tags
Constructing new vector spaces out of old ones rk tags
Bases and identity rk tags
Linear maps characteristics II rk tags
more (42 more)
Attributes & Decorations
Tags
eth, field, hs22, lineare algebra, proof, vector space
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Decoration
Content image