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Math Help - Rank of a matrix

  1. #1
    Member mybrohshi5's Avatar
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    Rank of a matrix

    Find the rank of the matrix

    A =  \begin{bmatrix}0&6\\0&-2\\0&5\end{bmatrix}

    I know that rank is just the number of pivots a matrix has when in reduced row echelon form, but this one is confusing to me.

    RREF A =  \begin{bmatrix}0&1\\0&0\\0&0\end{bmatrix}

    I thought this would have a rank of 0 because there are no pivots but i was wrong and it has a rank of 1.

    Why is this?

    Thanks for any help
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by mybrohshi5 View Post
    Find the rank of the matrix

    A =  \begin{bmatrix}0&6\\0&-2\\0&5\end{bmatrix}

    I know that rank is just the number of pivots a matrix has when in reduced row echelon form, but this one is confusing to me.

    RREF A =  \begin{bmatrix}0&1\\0&0\\0&0\end{bmatrix}

    I thought this would have a rank of 0 because there are no pivots but i was wrong and it has a rank of 1.

    Why is this?

    Thanks for any help
    The matrix RREF A has one "non-zero" row. that means the matrix A has one independent row vector. So its rank is 1.
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  3. #3
    Member mybrohshi5's Avatar
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    So finding rank is just the number of rows that has at least one non-zero entry in it?
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by mybrohshi5 View Post
    So finding rank is just the number of rows that has at least one non-zero entry in it?
    Yes, this is the way that I learnt to find the rank of a matrix. I would also suggest referring to linear independence


    Actually, the NUMBER of rows (in the RREF matrix) that are NON-ZERO is the RANK of the matrix. Here your matrix has one non-zero row, your rank is 1.
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  5. #5
    Member mybrohshi5's Avatar
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    Thanks that clears things up for me
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