1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook