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Math Help - Linear independence

  1. #1
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    Linear independence

    v=(6, -3, 0)
    u=(-3, 5, -7)
    w=(9, 6, k)

    what real number can't k be for the vectors to be linearly independent?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    What about calculating the determinant of the three vectors ? When it's null, the vectors are linearly dependent and it'll give you the condition on k.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by weasley74 View Post
    v=(6, -3, 0)
    u=(-3, 5, -7)
    w=(9, 6, k)

    what real number can't k be for the vectors to be linearly independent?
    set up the augmented matrix: \left( \begin{array}{ccc} \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right] &  \left[ \begin{array}{c} u_1 \\ u_2 \\ u_3 \end{array} \right] &   \left[ \begin{array}{c} w_1 \\ w_2 \\ w_3 \end{array} \right]  \end{array} \right) . equate it to zero and solve the system. the k for which the system only has the trivial solution is linearly independent
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  4. #4
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    I've tried all of this, and I keep getting the wrong answer.
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  5. #5
    Super Member flyingsquirrel's Avatar
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    Then write your answers here so that we can correct them.
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  6. #6
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    Talking

    I get that k can't be 21 for the vectors to be linearly independent, please correct me
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  7. #7
    Super Member flyingsquirrel's Avatar
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    Maybe should I have asked for the calculations instead of the answers ? (if you get k=21 check the signs, it might help)
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  8. #8
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    thanks! sign problem. jeez, i've been going crazy over this
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