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Math Help - Question on linear dependence: Where do I go wrong?

  1. #1
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    Question Question on linear dependence: Where do I go wrong?

    Hello,

    I tried to find a solution (see attachment) to the exercise in the attachment, but somehow I end up with two values for k that do not result in linear dependent vectors. Where do I go wrong? What SHOULD I do? And what are the right values for k?

    Please help!
    Attached Thumbnails Attached Thumbnails Question on linear dependence: Where do I go wrong?-exercise2.png   Question on linear dependence: Where do I go wrong?-solutionpart1.jpg   Question on linear dependence: Where do I go wrong?-solutionpart2.jpg  
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  2. #2
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    Re: Question on linear dependence: Where do I go wrong?

    you dropped a minus sign in the third row in the second column.

    what you should have ended up with, in the 3,3 position is:

    1 - \frac{4}{k} + \frac{3}{k} - \frac{2}{k^2}

    some additional comments:

    1) please make an effort to type your questions out. many people will not address problems that are entirely from images.
    2) since you divide by k several times in the course of the row-reduction, you should check before-hand that 0 is not a value that makes the set linearly dependent.
    3) rather than use the substitution x = 1/k, just get your expression over a common denominator. since this equals 0, you can just consider the numerator, and will not have to substitute back for k when you're done.
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  3. #3
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    Re: Question on linear dependence: Where do I go wrong?

    You are right! Thanks!
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