My Math Forum  

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

Linear Algebra Linear Algebra Math Forum


Thanks Tree1Thanks
  • 1 Post By Country Boy
Reply
 
LinkBack Thread Tools Display Modes
April 22nd, 2018, 05:23 AM   #1
Newbie
 
Joined: Apr 2018
From: Australia

Posts: 1
Thanks: 0

Bases of subspaces in $R^3$

How do I find the bases of the set of vectors on the line x/2 = y/3 = z/4?
harrietcheo is offline  
 
April 22nd, 2018, 12:19 PM   #2
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

$\displaystyle \frac{x}{2}= \frac{y}{3}= \frac{z}{4}$
Because this is a line, it is one- dimensional which means a basis consists of a single vector.
Taking x= y= z= 0, that condition becomes 0= 0= 0 which is true so (0, 0, 0) is a point on that line. Taking x= 2, y= 3, z= 4, that condition becomes 1= 1= 1 which is true so (2, 3, 4) is also a point on that line. The vector <2- 0, 3- 0, 4- 0>= <2, 3, 4> is a vector in the direction of that line so {<2, 3, 4>} is a basis for that line (more correctly, "is a basis for the vector space determined by that line.).
Thanks from SDK
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
$r3$, bases, subspaces



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Subspaces. JackPirri Linear Algebra 3 December 13th, 2017 06:54 AM
Subspaces Cloud Linear Algebra 0 October 25th, 2014 03:13 AM
Subspaces baz Linear Algebra 1 April 15th, 2013 06:19 PM
Linear Subspaces... Babaloo2u Linear Algebra 1 November 10th, 2010 04:33 AM
Subspaces remeday86 Linear Algebra 1 July 11th, 2010 11:27 AM





Copyright © 2018 My Math Forum. All rights reserved.