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Math Help - elementary matrix corresponding to row operations

  1. #1
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    elementary matrix corresponding to row operations

    I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

    We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

    for instance what would the elementary matrix be for

    | 1 3 | = | 1 3 |
    | 3 1 | = | 0 -8| (r2+-3r1)
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  2. #2
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    Try:

    1 0
    -3 1

    with this matrix multiplied from the left of your original matrix.
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  3. #3
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    Quote Originally Posted by qmech View Post
    Try:

    1 0
    -3 1

    with this matrix multiplied from the left of your original matrix.
    ah alright thanks
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  4. #4
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    Quote Originally Posted by Juggalomike View Post
    I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

    We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

    for instance what would the elementary matrix be for

    | 1 3 | = | 1 3 |
    | 3 1 | = | 0 -8| (r2+-3r1)
    More generally, elementary matrix corresponding to any row operation is the matrix you get by applying that row operation to the identity matrix.

    From \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}, subtracting 3 times the first row from the second gives \begin{bmatrix}1 & 0 \\ -3 & 1\end{bmatrix} as qmech says.
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  5. #5
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    Quote Originally Posted by Juggalomike View Post
    I just had a question on my final and i dont remember ever hearing of it(and judging by the fact that 2/3 my class was asking about it im not the only one)

    We where required to show the elementary matrix corresponding to each elementary row operation we performed while reducing a matrix ro rref.

    for instance what would the elementary matrix be for

    | 1 3 | = | 1 3 |
    | 3 1 | = | 0 -8| (r2+-3r1)


    \begin{pmatrix}1&0\\\!\!\!-3&1\end{pmatrix} , multiplication from the left, of course.

    Tonio
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