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Math Help - vector

  1. #1
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    vector

    Are the vectors
    <br />
6 , 3\sin^2 x , 2\cos^2 x<br />
in F(-infinity,infinity) the space of all functions from R to R linearly dependent or linearly independent?
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  2. #2
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    Been a while since I've done this, but if I recall (and it makes sense, given the terminology), if you can write one of the vectors as a linear combination of the other vectors, then they're not all linearly independent. If this assumption is incorrect, well, throw this post away.

    Note that we can rewrite 3sin^{2}x as 3(1-cos^{2}x) = 3 - 3cos^2{x}.

    That's certainly a combination of the others:

    3 is simply half the "6" vector, and the other part is 1.5 times the cosine-squared vector.

    So I vote that they are not linearly independent.
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  3. #3
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    Quote Originally Posted by 00hyvs45 View Post
    Are the vectors
    <br />
6 , 3\sin^2 x , 2\cos^2 x<br />
in F(-infinity,infinity) the space of all functions from R to R linearly dependent or linearly independent?
    I have answered this question in http://www.mathhelpforum.com/math-he...ly+independent. You could have asked me if you didnt understand, rather than editing the post
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