Exercise
https://texercises.com/exercise/direct-sums/
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:
Let VW be vector spaces over K. Then the cartesian product Vtimes W becomes a vector space over K if we ow it with the following operations: v_w_+v_w_&:v_+v_w_+w_ forall v_w_v_w_in Vtimes W alpha vw&: alpha valpha w forall alpha in K vwin Vtimes W _Vtimes W&: _V _Wquad textthe zero or neutral element of Vtimes W This new space Vtimes W is usually denoted Voplus W and is called the direct of V and W. We write the elements of Voplus W as vw or voplus w.

Solution:
Proof. Show that all the eight axioms of a vector space are satisfied.
Meta Information
\(\LaTeX\)-Code
Exercise:
Let VW be vector spaces over K. Then the cartesian product Vtimes W becomes a vector space over K if we ow it with the following operations: v_w_+v_w_&:v_+v_w_+w_ forall v_w_v_w_in Vtimes W alpha vw&: alpha valpha w forall alpha in K vwin Vtimes W _Vtimes W&: _V _Wquad textthe zero or neutral element of Vtimes W This new space Vtimes W is usually denoted Voplus W and is called the direct of V and W. We write the elements of Voplus W as vw or voplus w.

Solution:
Proof. Show that all the eight axioms of a vector space are satisfied.
Contained in these collections:

Attributes & Decorations
Tags
eth, hs22, lineare algebra, proof
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Creator rk
Decoration
File
Link