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 August 9th, 2015, 09:05 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, 01:45 PM #2 Global Moderator   Joined: May 2007 Posts: 6,556 Thanks: 600 It looks like it should be trivially obvious. Add polynomials and get a polynomial, similarly multiply a polynomial by a constant.
 August 10th, 2015, 02:25 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 02:29 PM.
 August 10th, 2015, 04:01 PM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 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 04:07 PM.

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