A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
LINEAR ALGEBRA :
Prove that the transformation LA:R^n R^m
induced by the m x n matrix A is linear.
 2 years ago
LINEAR ALGEBRA : Prove that the transformation LA:R^n R^m induced by the m x n matrix A is linear.

This Question is Closed

yakeyglee
 2 years ago
Best ResponseYou've already chosen the best response.1Linear transformations produced by matrices are defined as functions as follows. (here, taking your problem's example of transformation \(LA\)).\[LA(\vec x) = A\vec x\]Here, \(\vec x \in \mathbb R^n\) and \(A\vec x \in \mathbb R^m\), as you specified. Remember, if you want to show that \(f:A\rightarrow B\) is a linear transformation, you need to show that for all \(a_1, a_2 \in A\) and all constants \(C_1, C_2 \in \mathbb R\) that \[f(C_1a_1+C_2a_2)=C_1 f(a_1) + C_2 f(a_2).\]Does this give you enough information to proceed?

liliy
 2 years ago
Best ResponseYou've already chosen the best response.0wow, i dont really understand i tho. can u say it more in english than math lol

yakeyglee
 2 years ago
Best ResponseYou've already chosen the best response.1Try reading it slowly.
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.