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Homework Help: Linear Independence of a 3x3 matrix

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data
    A is a 3x3 matrix with distinct eigenvalues lambda(1), lambda(2), lambda(3) and corresponding eigenvectors u1,u2, u3.

    Suppose you already know that {u1, u2} is linearly independent.

    Prove that {u1, u2, u3} is linearly independent.

    2. Relevant equations

    3. The attempt at a solution
    I am supposed to prove that {u1, u2, u3} is linearly independent, but since there are distinct eigenvalues/vectors, is that not enough to say that {u1, u2, u3} is linearly independent?
  2. jcsd
  3. Apr 18, 2010 #2


    Staff: Mentor

    No, that's not enough. That's exactly what you need to prove.
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