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Homework Help: Matrices (rank, dim ect)

  1. Aug 14, 2010 #1
    (a)Determine the row rank of the matrix,

    1 1 1 1
    1 1 2 5
    2 2 0 -6

    (b) What is the column rank of this matrix?
    (c) What is the dimension of the solution space Mx=0

    So this is my answer:

    I have reduced my matrix into echelon form and i get

    1 1 1 1
    0 0 -1 -4
    0 0 0 0

    Therefore my row rank is 2 (the number of linearly independent rows)

    Since by rank theorem, (row rank = column rank = determinental rank) the column rank is also 2.

    And the dimension of the solution space is 2 (number of columns - rank)

    Is this answer correct?

    Thank you
    Dylan
     
  2. jcsd
  3. Aug 14, 2010 #2
    yes, i think so
     
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