A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
4. Let A ∈ F^m×n
. Show that if y ∈ F^1×n
is in the row space of A and
x ∈ F^n×1
is in the null space of A, then yx = 0
anonymous
 3 years ago
4. Let A ∈ F^m×n . Show that if y ∈ F^1×n is in the row space of A and x ∈ F^n×1 is in the null space of A, then yx = 0

This Question is Closed

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Well, if \(x\in \ker(A)\) (\(\ker(A)\) is the null space), then \(Ax=0\). Let \(A=(\vec{a_1},\vec{a_2},...,\vec{a_n})\) where each \(\vec{a_n}\) is the \(n\)th row vector. Since \(y\) is in the row space of A, we can say that \[y=r_1\vec{a_1}+...+r_n\vec{a_n}\]for some \(r_1,...,r_n\in F\).Then. \[yx=r1\vec{a_1}x+...+r_n\vec{a_n}x.\]Since \(Ax=0\), \(\vec{a_j}x=0\) for all \(1\le j\le n\), we can conclude that \(yx=0\). Did this make sense?
Ask your own question
Sign UpFind 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.