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Math Help - Rank of Matrix ??

  1. #1
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    Smile Rank of Matrix ??

    Can someone please explain "rank of matix" through example ????


    THANKS.....
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  2. #2
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    Quote Originally Posted by Sameera View Post
    Can someone please explain "rank of matix" through example ????


    THANKS.....
    The rank of a matrix is a dimension of the spam of the its rows.

    For example, consider:
    A=\begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 4 \\ 2&4&6 \end{bmatrix}

    The rows are:
    1) \bold{r}_1 = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix}
    2) \bold{r}_2 = \begin{bmatrix} 1 & 2 & 4 \end{bmatrix}
    3) \bold{r}_3 = \begin{bmatrix} 2 & 4 & 6 \end{bmatrix}

    We want to find the dimension of \text{spam}\{ \bold{r}_1, \bold{r}_2, \bold{r}_3 \}.

    Note that \bold{r}_3 = 2\bold{r}_1 therefore \text{spam}\{ \bold{r}_1,\bold{r}_2,\bold{r}_3 \} = \text{spam}\{ \bold{r}_1, \bold{r}_2\}.
    And \bold{r}_1,\bold{r}_2 are linearly independent since they are not proportional.
    Therefore, the dimension of \text{spam}\{\bold{r}_1,\bold{r}_2\} is 2.

    Therefore \text{rank}(A) = 2
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