A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Let A be a fixed vector in R^(nxn) and let S be the set of all matrices that commute with A; that is,
S={B  AB=BA}
Show that S is a subspace of R^(nxn).
 one year ago
Let A be a fixed vector in R^(nxn) and let S be the set of all matrices that commute with A; that is, S={B  AB=BA} Show that S is a subspace of R^(nxn).

This Question is Open

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1what do you need to show in order to show something is a subspace of a vector space?

Omar91X
 one year ago
Best ResponseYou've already chosen the best response.0All I know is that the subset has to satisfy two conditions. That is what I am not sure how to start.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1i think you only need to show two things 1) if \(w, v\in S\) then \(w+v\in S\) and 2) if \(w \in S, \lambda\in \mathbb{R}\) then \(\lambda w\in S\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1i guess i should have written it with capital letters, but that is the idea

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1so you have two jobs 1) show that if \(B, C\) commute with \(A\), that is if \(AB=BA\) and \(AC=CA\) then \[A(B+C)=(B+C)A\] i.e. show that if \(B\in S\) and \(C\in S\) then \(B+C\in S\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1this should be straight forward because of the distributive law

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1you also have to show if \(AB=BA\) then \(A\lambda B=\lambda BA\) which again should be straight forward by the definition of scalar multiplication

Omar91X
 one year ago
Best ResponseYou've already chosen the best response.0This answers every question I had. Thanks for taking your time. And then I just realized how simple this should've been.

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1goal of course is to take the general definition and apply it in the specific case that is the hard part, rest is routine
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.