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Homework Help: Generalized solutions for the smallest Euclidean norm

  1. Oct 9, 2006 #1
    Hi folks,

    I have to find the generalized solution for the following Ax=y :

    [1 2 3 4;0 -1 -2 2;0 0 0 1]x=[3;2;1]

    The rank of A is 3 so there is one nullity so the generalized solution is:

    X= x+alpha.n (where alpha is a constant , and n represents the nullity)

    I found the solution to be:

    X= [-1;0;0;1]+ alpha [1;-2;1;0] which is a non-unique solution.

    I need to find (alpha) so that the generalized solution, i.e, the eigenvector has the smallest Euclidean norm

  2. jcsd
  3. Oct 10, 2006 #2
    Any help ?
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