Exercise
https://texercises.com/exercise/span-first-definition/
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 V be a vector space over K. Let W_i_iin I be a collection of subspaces W_isubseteq V of V indexed by iin I I is a set of indices. Then W:bigcap_i in I W_i is a linear subspace of V.

Solution:
Proof. in W because in W_i forall i in I. Let a_a_ in K v_v_ in W. We want to show a_v_+a_v_ in W. Let j in I. Since v_v_ in bigcap_i in I W_i we have v_v_ in W_j Longrightarrow a_v_+a_v_ in W_j because W_j subseteq V is a subspace. We have proven that forall jin Iquad a_v_+a_v_in W_j Longrightarrow a_v_+a_v_ in bigcap_i in I W_iW which is what we wanted to show in the ning.
Meta Information
\(\LaTeX\)-Code
Exercise:
Let V be a vector space over K. Let W_i_iin I be a collection of subspaces W_isubseteq V of V indexed by iin I I is a set of indices. Then W:bigcap_i in I W_i is a linear subspace of V.

Solution:
Proof. in W because in W_i forall i in I. Let a_a_ in K v_v_ in W. We want to show a_v_+a_v_ in W. Let j in I. Since v_v_ in bigcap_i in I W_i we have v_v_ in W_j Longrightarrow a_v_+a_v_ in W_j because W_j subseteq V is a subspace. We have proven that forall jin Iquad a_v_+a_v_in W_j Longrightarrow a_v_+a_v_ in bigcap_i in I W_iW which is what we wanted to show in the ning.
Contained in these collections:

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