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Linear Algebra - find rk(A)

  1. Jul 19, 2012 #1
    1. The problem statement, all variables and given/known data

    find rk(A) for the following matrix

    [3 -6]
    [5 -10]
    [-2 4]

    2. Relevant equations
    3. The attempt at a solution

    How am I supposed to find the answer when I don't know what r is? I thought r had to be a number or a scalar and you multiply the whole matrix by it.
     
  2. jcsd
  3. Jul 19, 2012 #2
    rk(A) is the rank of A, which is the dimension of the image of the matrix, or, equivalently, the number of linearly independent columns in the matrix.
     
  4. Jul 19, 2012 #3
    ok, got it, but you can easily see how that could throw one off when given the following theorem:

    Screenshot2012-07-19at23441AM.png
     
  5. Jul 19, 2012 #4
    Not really. Didn't your book define rk(A)? The theorem was about dot products.
     
  6. Jul 19, 2012 #5
    A point that might help here as far as notation goes: usually, functions like sine, cosine, and rank are written in fully upright, non-italic, non-bold letters, e.g. [itex]\sin \theta[/itex] or [itex]\text{rk}(A)[/itex]. Scalar variables, on the other hand, will usually be italicized. [itex]rk[/itex] is the product of the variables [itex]r[/itex] and [itex]k[/itex].
     
  7. Jul 19, 2012 #6
    When you're coming across new notation it's easy to get them confused.
     
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