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Dimension of row/ column space

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    In the following exercises verify that the row rank is equal to the column rank by explicitly finding the dimensions of the row space and the column space of the given matrix.

    A = [1 2 1 ; 2 1 -1]


    2. Relevant equations



    3. The attempt at a solution

    All i can think of is just row reduce it to row echelon form and then find the rank of the matrix. How do i do it explicitly?
     
  2. jcsd
  3. Jan 25, 2009 #2
    1. Show that the rows of A are not linear combinations of each other, i.e. one is the multiple of the other.

    2. Show that one column is the linear combination of the other 2 columns. Then show that the remaining 2 columns are not a multiple of the other.

    then you've explicitly shown that the rank(A) = row rank (A) = column rank (A)
     
  4. Jan 25, 2009 #3
    Do you mean by one is NOT the multiple of the other?
     
  5. Jan 25, 2009 #4
    You are quite correct. I did not proofread before submitting.
     
  6. Jan 25, 2009 #5
    Okay, thanks. Now that make sense =D
     
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