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Homework Help: Dimension of matrix

  1. May 23, 2012 #1


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    1. The problem statement, all variables and given/known data
    [tex]A= \begin{bmatrix}1 & 1 & 1 & 1 \\ 2 & 1 & 0 & -1 \\ 3 & 4 & 5 & 6 \\ -1 &2 &1&0 \end{bmatrix}[/tex]Determine the dimension of A and give a set of basis vectors for A.

    2. Relevant equations
    Dimension of matrix, ref form of matrix.

    3. The attempt at a solution
    I reduced the matrix to row echelon form and then the dimension = rank of matrix. Is that correct? I am quite confused about what dimension means. In a 4x4 matrix, maybe dimension is 16? or is it the number of non-zero matrix elements?
  2. jcsd
  3. May 23, 2012 #2
    Easy way to remember it is:

    # of columns - # of non zero rows in rref
  4. May 23, 2012 #3


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    So, the dimension of A is the rank of the matrix A?
  5. May 23, 2012 #4


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    Yes. In fact, I would consider the term "dimension of a matrix" very strange. The rank of a matrix is the dimension of the image of the matrix.
  6. May 23, 2012 #5
    I think by dimension you mean "nullity" cause our lecturer also used "dimension of a matrix" which was confusing when studying from other sources.

    Try plugging your matrix in wolfram and ask for nullity.

    In the output it states a "dimension" which is always exactly what I always needed. So maybe that's what it means.
  7. May 23, 2012 #6

    Ray Vickson

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    How does your textbook or lecturer or course notes define the term "dimension of a matrix"?

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