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Sourav posted an Question
July 15, 2020 • 03:23 am 30 points
  • IIT JAM
  • Mathematics (MA)

Let, g:-1, 1] - r, f) = x', gr) = x2|x| then qfand g are linearly independent on [-1,1} fand g are linearly dependent on [-1, 1] ac) s) g(x)-f) gt) is not ident

Let, g:-1, 1] - R, f) = x', gr) = x2|x| Then Qfand g are linearly independent on [-1,1} fand g are linearly dependent on [-1, 1] AC) S) g(x)-f) gt) is NOT Identically zero on [-1, 1] (There exist continuous function p(x) and q(x) such that fand g satisfy +py + qy = 0 on [- 1,

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    Arzoo Best Answer

    Attachment 2

    cropped170490393488426628.jpg
    cropped3404429414125352161.jpg
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    in 2nd pic you say f&g L.D

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    but 1st you say L.I

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    in 2nd pic, i mistakenly write l.d., But rest of the explanation is right. So make correction.

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    w=0 nd f,g are L.I. i.e. p and q can't be continuous

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