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Math Help - Rank, and Row Multiple Examples

  1. #1
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    Post Rank, and Row Multiple Examples

    is it possible to have a system satifying this:
    A system of four equations in three variables such that the associated coecient matrix has no zero

    entries, no row is a multiple of any other row, and the matrix has rank 2?

    i thought that if no row is a multiple of any other than how could u get anything other than rank 3??

    I also need to somehow come up with examples of:

    A system of three equations in four variables such that the associated coeffcient matrix has no zero
    entries, no row is a multiple of any other row, and the matrix has rank 2.



    A system of three equations in four variables such that the associated coefficient matrix has no zero entries
    and has rank 3.


    not sure what examples satify the above but any help would be much appreciated as this is all very new to me.

    cheers

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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by situation View Post
    is it possible to have a system satifying this:
    A system of four equations in three variables such that the associated coecient matrix has no zero

    entries, no row is a multiple of any other row, and the matrix has rank 2?

    i thought that if no row is a multiple of any other than how could u get anything other than rank 3??

    I also need to somehow come up with examples of:

    A system of three equations in four variables such that the associated coeffcient matrix has no zero
    entries, no row is a multiple of any other row, and the matrix has rank 2.



    A system of three equations in four variables such that the associated coefficient matrix has no zero entries
    and has rank 3.


    not sure what examples satify the above but any help would be much appreciated as this is all very new to me.

    cheers

    1) A=\left[ \begin{array}{cccc} 1 & 2 & 3 \\ 5 & 6 & 7 \\ 6 & 8 & 10 \\ 7 & 10 & 13 \end{array} \right]

    (R3=R1+R2, R4=2R1+R2)

    Try 2) and 3) yourself.
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  3. #3
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    Quote Originally Posted by alexmahone View Post
    1) A=\left[ \begin{array}{cccc} 1 & 2 & 3 \\ 5 & 6 & 7 \\ 6 & 8 & 10 \\ 7 & 10 & 13 \end{array} \right]

    (R3=R1+R2, R4=2R1+R2)

    Try 2) and 3) yourself.
    ok thanks for that. for part 2 i get B=\left[ \begin{array}{cccc} 1 & 2 & 3 & 5 \\  6 & 7 & 8 & 9  \\ 7 & 9 & 11 & 14 \end{array} \right]

    is that correct??
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by situation View Post
    ok thanks for that. for part 2 i get B=\left[ \begin{array}{cccc} 1 & 2 & 3 & 5 \\  6 & 7 & 8 & 9  \\ 7 & 9 & 11 & 14 \end{array} \right]

    is that correct??
    Yes.
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