August 9th, 2015, 10:05 AM  #1 
Member Joined: Mar 2015 From: Brasil Posts: 90 Thanks: 4  Vector Spaces
Prove that P (ℝ), the set of polynomials, is a vector space with the usual operations of addition and multiplication of polynomials of a scalar by a polynomial.

August 9th, 2015, 02:45 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,660 Thanks: 648 
It looks like it should be trivially obvious. Add polynomials and get a polynomial, similarly multiply a polynomial by a constant.

August 10th, 2015, 03:25 PM  #3 
Member Joined: Mar 2015 From: Brasil Posts: 90 Thanks: 4  Vector Space
If u, v and w are vectors of a vector space V such that u + w= v+w, show that u = v.
Last edited by Luiz; August 10th, 2015 at 03:29 PM. 
August 10th, 2015, 05:01 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
I am puzzled by this. You are asking about Linear Algebra so I would expect that you would know the definition of a vector space. And that should be enough answer your questions. One part of the definition of "vector space" is that it forms a "group" with respect to addition and part of the definition of "group" is that it contains negatives (additive inverses). Last edited by Country Boy; August 10th, 2015 at 05:07 PM. 

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