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August 9th, 2015, 09:05 AM   #1
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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.
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August 9th, 2015, 01:45 PM   #2
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It looks like it should be trivially obvious. Add polynomials and get a polynomial, similarly multiply a polynomial by a constant.
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August 10th, 2015, 02:25 PM   #3
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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.
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August 10th, 2015, 04:01 PM   #4
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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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