My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 24th, 2015, 08:42 AM   #1
Member
 
Joined: Mar 2015
From: Brasil

Posts: 90
Thanks: 4

Linear Independence and Linear Dependence.

If $\left \{ u,v \right \}$, $\left \{ v,w \right \}$ and $\left \{ w,u \right \}$ LI are subsets of a vector space V, then $\left \{ u,v,w \right \}$ is LI?
Note: LI is Linear Independence.
Luiz is offline  
 
August 24th, 2015, 10:19 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,937
Thanks: 2265

Math Focus: Mainly analysis and algebra
What happens if $\vec u$, $\vec v$ and $\vec w$ are co-planar? Can they be distinct and co-planar?

Last edited by skipjack; August 24th, 2015 at 11:24 AM.
v8archie is offline  
August 24th, 2015, 11:18 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,647
Thanks: 680

(1, 0) and (0, 1) are linearly independent.
(1, 0) and (1, 1) are linearly independent.
(0, 1) and (1, 1) are linearly independent.
Country Boy is offline  
August 24th, 2015, 01:44 PM   #4
Member
 
Joined: Mar 2015
From: Brasil

Posts: 90
Thanks: 4

No, if it is co-planar they would LD (linear dependent). and q I do now ????
Luiz is offline  
August 24th, 2015, 02:05 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,937
Thanks: 2265

Math Focus: Mainly analysis and algebra
So you have that, if the three vectors are co-planar, they would be LD.
Can you find three co-planar vectors that, pairwise are LI? Hint: see Country Boy's post.

Last edited by v8archie; August 24th, 2015 at 02:08 PM.
v8archie is offline  
August 24th, 2015, 02:10 PM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,937
Thanks: 2265

Math Focus: Mainly analysis and algebra
The general case of Country Boy's example would be $\vec w = a\vec u + b \vec v$ where $a$ and $b$ are non-zero real numbers. The main advantage of writing it like this is that we get any number of dimensions for free with the notation.
v8archie is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
dependence, independence, linear



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear Independence and Linear Dependence. Luiz Linear Algebra 1 August 24th, 2015 10:45 AM
Linear independence & linear dependence autumn94 Linear Algebra 1 March 29th, 2015 02:14 PM
Determine linear dependence over Z2 phongchaychua Linear Algebra 2 April 27th, 2014 05:08 AM
Linear Dependence Equation Spennet Linear Algebra 2 August 18th, 2011 08:00 AM
Linear Dependence Proof Singularity Linear Algebra 1 February 4th, 2010 05:32 PM





Copyright © 2017 My Math Forum. All rights reserved.