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Math Help - About Gaussian Elimination

  1. #1
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    Question About Gaussian Elimination

    I've studied about matrix for 1 semester.
    And now, I'm studying about Gaussian Elimination in Matrix Equation.
    we have to compose the augmented matrix equation, right? the proportion of the matrix of numeral coefficients and the answer of the equation will equal to the matrix of the variables.

    But!! Yesterday, my teacher gave me the problem like this:
    x+y-z
    y+z-x
    -z+x-y
    And he didn't give anymore he didn't give that each equation equals to how many...he said that I have to do by using Gaussian Elimination. I don't know how to solve it. Please help me....

    Thanks
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  2. #2
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    Quote Originally Posted by sallsa View Post
    I've studied about matrix for 1 semester.
    And now, I'm studying about Gaussian Elimination in Matrix Equation.
    we have to compose the augmented matrix equation, right? the proportion of the matrix of numeral coefficients and the answer of the equation will equal to the matrix of the variables.

    But!! Yesterday, my teacher gave me the problem like this:
    x+y-z
    y+z-x
    -z+x-y
    And he didn't give anymore he didn't give that each equation equals to how many...he said that I have to do by using Gaussian Elimination. I don't know how to solve it. Please help me....

    Thanks
    Line "x's with "x's "y's with "y's and "z's" with "z's"

    I think he wants you to transform,
    \left[ \begin{array}{ccc}1&1&-1\\ -1&1&1\\ 1&-1&-1 \end{array} \right]
    Into an inverse matrix by using elementary row operations.
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  3. #3
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    Lexington, MA (USA)
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    Hello, sallsa!

    Yesterday, my teacher gave me the problem like this:
    . . \begin{array}{ccc}x+y-z \\ y+z-x \\ -z+x-y\end{array}

    And he didn't give anymore he didn't give that each equation equals to how many.
    He said that I have to do by using Gaussian Elimination.

    Is your teacher known for his sense of humor?
    Even if he gave you the constant terms, this system has no solution.

    Look at the augmented matrix:

    . . \begin{bmatrix}1 & 1 & \text{-}1 & | & a \\ \text{-}1 & 1 & 1 & | & b \\ 1 & \text{-}1 & \text{-}1 & | & c\end{bmatrix}

    The determinant of the coefficients is zero. .Also, Row 2 plus Row 3 zeros-out.

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