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Homework Help: Define the matrix?

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Let S = { u1, u2, u3} be an orthogonal set of nonzero vectors in R3. Define (3 x 3) matrix A by A = [u1, u2, u3]. Show that A is nonsingular and A'A (' is transpose) is a diagonal matrix. Calculate the diagonal matrix using the given orthogonal vectors: u1 = [1 1 1]'; u2 = [-1 0 1]'; u3 = [-1 2 -1]'

    2. Relevant equations


    3. The attempt at a solution

    I think my IQ drops by the minute, thereof a stupid question.... what does it mean to "define" the matrix? Do I just create the matrix from the given set of vectors??
    Last edited: Feb 23, 2010
  2. jcsd
  3. Feb 23, 2010 #2


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    Homework Helper

    Yes, exactly.

    Now, what is the relation between orthogonality and linear independence of vectors? Further on, how does this relate to the matrix rank? And how does the rank relate to regularity/non-singularity?
  4. Feb 24, 2010 #3
    could i just say that since the vectors are orthogonal, that means they are linearly independent, and that makes the matrix non singular.. sounds pretty logical to me :)
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