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How to find basis vectors for a+ ax^2+bx^4?

  1. Feb 17, 2016 #1
    I want to find basis for a+ax^2+bx^4 belong to p4.
    I am getting the following result is it right?
    =>a(1+x^2) + b(x^4)
    => basis ={1+x^2, x^4}

    Is that right ? Please help me any help is appreciated.
  2. jcsd
  3. Feb 17, 2016 #2


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    Homework Helper

    Since you only have two terms (a,b) it makes sense to have a basis with two vectors. This function will be in the span of those bases for any choice of a and b.
    In the standard polynomial basis [1, x, x^2, x^3, x^4,x^5 ... ], this would be [ a, 0, a, 0, b,0,...].
  4. Feb 17, 2016 #3
    Thank you so much.
  5. Feb 18, 2016 #4
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