My Math Forum  

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

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
March 2nd, 2009, 12:44 PM   #1
Joined: Mar 2009

Posts: 3
Thanks: 0

Linear Algebra.Linear Transformations.Help!!

The problem is: "Let S a linear transformation from R^3 to R^2 and T a linear transformation from R^2 to R^3. Show that TS is not invertible." Have anyone can help me to the above problem. Thanks anyone in advance.
ypatia is offline  
March 2nd, 2009, 06:28 PM   #2
Joined: Jan 2009

Posts: 72
Thanks: 0

Re: Linear Algebra.Linear Transformations.Help!!

There is an infinity of vectors (in fact a 1-dimensional manifold) in R3 that are preimages of any vector in the range of TS. Thus, TS cannot be 1-1 (i.e., it's not injective) and therefore has no left inverse. Since an inverse is necessarily a left inverse, there can be no inverse.
signaldoc is offline  

  My Math Forum > College Math Forum > Linear Algebra

algebralinear, linear, transformationshelp

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear Transformations in Linear algebra matqkks Linear Algebra 1 February 7th, 2012 01:39 PM
Linear Map transformations azelio Linear Algebra 0 October 19th, 2011 06:59 AM
Linear transformations nuke Linear Algebra 3 April 14th, 2011 12:32 PM
Linear transformations TsAmE Linear Algebra 0 October 9th, 2010 06:54 AM
Linear Transformations wontonsoup Linear Algebra 2 May 25th, 2009 04:35 PM

Copyright © 2019 My Math Forum. All rights reserved.