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

  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,]

    Last edited: Dec 4, 2011
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,268
    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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