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Values for which a set of vectors form a basis of Rn

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    For what value(s) of λ is the set of vectors {(λ^2-5, 1, 0), (2, -2, 3), (2, -3, -3)} form a basis of ℝ^3


    2. Relevant equations

    in order for a vector to form a basis it has to span R3 and the set has to be linearly independent.


    3. The attempt at a solution
    i tried doing row reduction on the matrix but i end up with identity matrix.
    which means it would be a basis for any value, which is impossible.

    the matrix I'm getting is [1, 0, 0 ; 0, 1, 0; λ^2 -5, 0, 4,]


    anybody??
     
    Last edited: Dec 4, 2011
  2. jcsd
  3. Dec 5, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What do you mean you get the identity matrix when you then write "the matrix I'm getting is [1, 0, 0 ; 0, 1, 0; λ^2 -5, 0, 4,]"? That's not row reduced. Or, rather, it is row reduced if and only if λ^2 -5= 0.
     
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