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Matrix with an Unknown

  1. Mar 3, 2010 #1
    I have the following matrix C =

    3 2 1 9
    4 2 6 12
    1 4 -3 3
    0 1 8 (3-b)

    y1=[-1 -1 1 -1] transpose

    For the vector y, I need to find all values of b such that the system of equations y=Cx has no unique solutions. Can someone help....

    Thanks
     
  2. jcsd
  3. Mar 3, 2010 #2

    radou

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    What is the relation between the system determinant and the uniqueness of the solution?
     
  4. Mar 3, 2010 #3
    I am not sure...I thought the system determinant is only used to find the interdependency of the basis. If there exist such a relation as you have mentioned....that is not mentioned in the question; so we can assume anything for the problem.
     
  5. Mar 3, 2010 #4
    By the way in order to have a unique solution r(A), rank equals n. But we know n but I don't know how to get rank!
     
  6. Mar 5, 2010 #5
    Notice how if b = 3 then column 4 becomes a multible of column 1. This solution would make the rank(C) < n = 4 and therfore C would not have an inverse making the system have no unique solitions.
     
  7. Mar 5, 2010 #6
    Thanks Live2Learn.......I got it!!!
     
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