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Math Help - Gram Schmidt Orthogonalization with functions

  1. #1
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    Gram Schmidt Orthogonalization with functions

    Hi. I have a quick question. Seems so simple, but for some reason I can't figure out how to start:

    Consider the vector space of continuous functions on the interval [0,1]. We define the scalar product of two such functions f, g by the rule:

    <f, g> = integral from 0 -> 1 of f(t)g(t) dt.

    Let V be the subspace of functions generated by the two functions f(t) = t and g(t) = t^2. Find an orthonormal basis for V.

    The part I'm stuck on is.. what do I start with? (what's v_1?) The answer key says rad 3 * t, but I'm not sure how the book got that.

    Thank you!
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  2. #2
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    Let t be v1. Then normalize v1 and solve v2
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  3. #3
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    gottt it. darn i feel dumb. thank you
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