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.
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
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

Similar exercises (49)
Title Creator Matched on
Span additional rk tags
Span and linear combinations rk tags
Basis and span rk tags
Basis and linear dependence rk tags
Group characteristics rk tags
more (44 more)
Attributes & Decorations
Tags
eth, hs22, lineare algebra, proof, span
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Proof
Decoration
Content image