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Math Help - Linear Independent problem

  1. #1
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    Linear Independent problem

    Hello, I am having some trouble proving
    that the set {1,x,x^2,x^3,...x^n} is linearly independent in Pn(R).
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    Quote Originally Posted by lllll View Post
    Hello, I am having some trouble proving
    that the set {1,x,x^2,x^3,...x^n} is linearly independent in Pn(R).
    If a_0 + a_1x+a_2x^2+...+a_nx^n = \bold{0} where \bold{0} is the zero function. It means that we have a polynomial always equaling 0 for any x. It means that that it must be the zero polynomial because otherwise we have a non-zero polynomial having infinitely many zero (for any x) which is impossible (it can have at most n zeros). Thus, a_0,...,a_n have to be all zero.
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