Thread: Vector Space question
View Single Post
  #2  
Old June 20th, 2008, 01:43 PM
flyingsquirrel's Avatar
flyingsquirrel flyingsquirrel is offline
Super Member
  
Join Date: Apr 2008
Posts: 789
Thanks: 152
Thanked 425 Times in 358 Posts
flyingsquirrel is a glorious beacon of lightflyingsquirrel is a glorious beacon of lightflyingsquirrel is a glorious beacon of lightflyingsquirrel is a glorious beacon of lightflyingsquirrel is a glorious beacon of light
Default
Hi
Quote:
Originally Posted by Kim Nu View Post
Could someone explain to me why the set of all elements of R^3 with the first component of 1 is not a real vector space? I'm lost on this one. Thanks,
It can't be a vector space because this set is not closed under addition :

\begin{pmatrix} 1\\ 0\\ 0 \end{pmatrix} +\begin{pmatrix} 1\\ 0\\ 0 \end{pmatrix}=\begin{pmatrix} 2\\ 0\\ 0 \end{pmatrix}
Reply With Quote