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Homework Help: Perpendicular vector

  1. Feb 17, 2007 #1
    1. The problem statement, all variables and given/known data
    how do I find the basis for all vectors that are perpendicular to both
    v1 = (1,1,0,0) and
    v2 = (1,0,1,1)

    If it were 3-D I could find a normal vector via cross product, but in n-dimensions.... what do I do?

    My one thought is to arrange and solve linear homogeneous system:
    [v1][x] = 0
    [v2][y] = 0

    since RHS is the dot product of the row vector (v1 or v2) and the column [x,y]t, and for vectors to be perpendicular, their dot product should be 0.
    Is that correct?

    Thanks in advance.
     
  2. jcsd
  3. Feb 17, 2007 #2

    quasar987

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    Science Advisor
    Homework Helper
    Gold Member

    If I understood correctly and you intend to solve the matrix equation

    [tex]\left(
    \begin{array}{cccc}
    1 & 1 & 0 & 0\\
    1 & 0 & 1 & 1
    \end{array}
    \right)\left(
    \begin{array}{c}
    x_1&x_2&x_3&x_4
    \end{array}\right)=
    \left(\begin{array}{c}
    0&0
    \end{array}
    \right)[/tex]

    then this is what I would do also.
     
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