Examples of vector spaces part II

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We look at examples of vector spaces whose elements are real valued functions, including vector spaces of polynomials.
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prof lee you sound really 'mellowed' here than in class. haha kinda not used to this version of you 

aroon
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AT 7:48 I don't get why there is a negative? Why does the first degree does not have a negative also?

ednakazuya
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Polynomials up to N degree is a valid Vector Space but Polynomial with 2 degree is not.Now If I take N=2 in first statement then first and second statement contradicting each other. Please solve my doubt?

mauliksoni