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Math Help - coordinates given basis

  1. #1
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    coordinates given basis

    I am stuck on this problem, i tried multiplying p(x) by B but the answer i got is incorrect, any help is appreciated

    The set is a basis for . Find the coordinates of relative to this basis:


    [p(x)]B=
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  2. #2
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    Quote Originally Posted by Juggalomike View Post
    I am stuck on this problem, i tried multiplying p(x) by B but the answer i got is incorrect, any help is appreciated

    The set is a basis for . Find the coordinates of relative to this basis:


    [p(x)]B=
    You are looking for c_1,c_2,c_3 such that

    c_1(-1+4x^2)+c_2(-3+4x+12x^2)+c_3(-7+8x+36x^2)=-28+36x+144x^2

    Expanding this out gives

    (-c_1-3_2-7c_3)\cdot 1+(4c_2+8c_3)\cdot x+(4c_1+12c_2+36c_3)\cdot x^2=-28+36x+144x^2

    Now just solve the system of equations for the needed coeffients.
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  3. #3
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    im confused, do you meen solve for c1 c2 and c3? or 1 x and x^2? Also, when solving for that coefficient do i set the others to 0?
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