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Math Help - Basis for orthognal vector

  1. #1
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    Basis for orthognal vector

    In R3 let S=span((1,2,4)^T)

    What is a basis for S^(perpendicular)?

    I know that 0=x*y=1y1+2y2+4y3

    and that y2 and y3 are free variables so y1=-2y2-4y3

    i have then tried to solve for each of the vectors this way but it is not correct.

    Please help?

    Thank You,
    Diggidy
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  2. #2
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    Quote Originally Posted by Diggidy View Post
    In R3 let S=span((1,2,4)^T)

    What is a basis for S^(perpendicular)?

    I know that 0=x*y=1y1+2y2+4y3

    and that y2 and y3 are free variables so y1=-2y2-4y3

    i have then tried to solve for each of the vectors this way but it is not correct.

    Please help?

    Thank You,
    Diggidy
    You have not solved the system correctly.

    y_1+2y_2+4y_3=0

    Now let y_3=s,y_2=t,y_1=-2t-4s

    Now we have the vector

    \begin{pmatrix} -2t-4s \\ t \\s \end{pmatrix}=t\begin{pmatrix} -2 \\ 1 \\ 0 \end{pmatrix}+s\begin{pmatrix} -4 \\ 0 \\ 1 \end{pmatrix}

    These two vectors will do the job.
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    You have not solved the system correctly.

    y_1+2y_2+4y_3=0

    Now let y_3=s,y_2=t,y_1=-2t-4s

    Now we have the vector

    \begin{pmatrix} -2t-4s \\ t \\s \end{pmatrix}=t\begin{pmatrix} -2 \\ 1 \\ 0 \end{pmatrix}+s\begin{pmatrix} -4 \\ 0 \\ 1 \end{pmatrix}

    These two vectors will do the job.
    O, i see, Thank you very much
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