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Homework Help: Rank of 5x3 matrix A is 3, what is RREF(A)?

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data
    Matrix A is of size 5x3 (5 rows and 3 columns) with rank(A)=3. Find the reduced row echlon form of A

    3. The attempt at a solution
    Rank(A)=3 thus, there are 3 pivot variables. Since there are 3 pivot variables and 3 columns=> no free variables, thus we have 2 rows of zeroes at the bottom. The top 3 rows represent a 3x3 identity matrix.

    It seems like the answer is just
    1 0 0
    0 1 0
    0 0 1
    0 0 0
    0 0 0
    Could someone please verify?

    I was curious if the question was instead a 3x5 matrix.
    For this scenario I observe the following:
    1) There will be 3 pivots, but since there are 5 columns, there will be 2 free variables.
    2) I think RREF(A) can be 4!=4*3*2=24 different matrices?
  2. jcsd
  3. Jan 26, 2015 #2


    Staff: Mentor

    Sure, this is fine.
    And the rank is still 3?
    Actually, there will be an infinite number of matrices. There would be two columns that could have any values.
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