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Math Help - [SOLVED] Elementary Matrices

  1. #1
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    [SOLVED] Elementary Matrices

    Which two elementary operations transform the following matrix:
    Code:
         2    -6     3    -3    -6
         4    -2    -6    -6     0
        -1    -3    -9     6     4
         7     3     3    -9     2
    Into this one:
    Code:
         2    -6     3    -3    -6
         4    -2    -6    -6     0
       -27    99   -18    27    78
         7     3     3    -9     2
    Thanks for any help!
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  2. #2
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    Quote Originally Posted by Incanus View Post
    Which two elementary operations transform the following matrix:
    Code:
         2    -6     3    -3    -6
         4    -2    -6    -6     0
        -1    -3    -9     6     4
         7     3     3    -9     2
    Into this one:
    Code:
         2    -6     3    -3    -6
         4    -2    -6    -6     0
       -27    99   -18    27    78
         7     3     3    -9     2
    Thanks for any help!
    What exactly your difficulty? I see that only the third row has changed so whatever elementary operations (row operations) are done must be done to it. There are three types of row operations: swap two rows (obviously not here), multiply one row by number, add a multiple of one row to another.

    You might try this: if we were to multiply the row by a, then add b times the first row, the first number would be -a+ 2b= -27 and the second number would be -3a- 6b= 99. That gives two equations to solve for a and b. Now try the third number: For those values of a and b, is -9a+ 3b= -18? If yes, check the other numbers but you are probably done. If not try b times the second row: -a+ 4b= -27, -3a-2b= 99, etc.
    If none of those work, then it must be that "add a multiple of one row to the third row" was used twice: Try a times the first row pluls b times the second row added to the third: 2a+ 4b- 1= -27, 2a- 2b- 3= 99, again two equations in two unknowns that can be checked by the other numbers in the third row.
    Tedious, but just algebra.
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  3. #3
    Super Member

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    Hello, Incanus!

    Never seen a guessing game with matrices.
    Wonder what the purpose of the problem is?



    Which two elementary operations transform

    this matrix . \begin{pmatrix}2 &\text{-}6&3&\text{-}3&\text{-}6\\ 4&\text{-}2&\text{-}6&\text{-}6&0\\ \text{-}1&\text{-}3&\text{-}9&6&4\\ 7&3&3&\text{-}9&2\end{pmatrix} . into this one: . \begin{pmatrix}2&\text{-}6&3&\text{-}3&\text{-}6\\ 4&\text{-}2&\text{-}6&\text{-}6&0\\ \text{-}27 &99&\text{-}18&27&78\\ 7&3&3&\text{-}9&2\end{pmatrix}

    . . \begin{array}{c}\text{Multiply }R_3\text{ by -3.} \\ \\[-4mm]<br />
\text{Multiply }R_1\text{ by -15.} \\ \\[-4mm]<br />
\text{Add and replace }R_3. \end{array}

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