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Find the orthogonal projection

  1. Jun 6, 2007 #1
    1. The problem statement, all variables and given/known data

    My questions is this:
    How to find the orthogonal projection of vector y= (7,-4,-1,2) on null space
    N(A)

    Where A is a matrix
    A =

    [tex]\left(\begin{array}{cccc}2&1&1&3\\3&2&2&1\\1&2&2&-9\end{array}\right)[/tex]

    2. Relevant equations

    [tex]A^TA\overline{x}=A^T\overline{y}[/tex]

    3. The attempt at a solution
    First I found the Null space of matrix A:
    A =

    [tex]\left(\begin{array}{cc}0&-5\\-1&7\\1&0\\0&1\end{array}\right)[/tex]

    Then, I applied he formula from aboce:

    A^TA =
    2 -7
    -7 75

    A^Ty= (3,-61)

    after that built an equation to find x:

    [tex]\left(\begin{array}{cc}2&-7\\-7&75\end{array}\right) \left(\begin{array}{c}X1\\X2\end{array}\right) = \left(\begin{array}{c}3\\-61\end{array}\right)[/tex]

    x1 = -2 , x2=-1
    P(x) = (5,-5,-2,-1)

    But the answer is:
    3/2(0,-1,1,0)

    What is wrong?
     
    Last edited: Jun 6, 2007
  2. jcsd
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