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Math Help - Finding the inverse of a matrix

  1. #1
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    Finding the inverse of a matrix

    So I'm trying to find the inverse of the matrix:

    [2 4 2]
    [2 5 2]
    [0 2 -1]

    I've gotten up to this bit:

    [1 0 5 | -1/2 -2 0]
    [0 1 -2| 1/2 1 0]
    [0 0 -3| 1 2 -1]

    I can't figure out how to get a 1 on the bottom right corner or the remaining two 0's. Help would be appreciated!
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  2. #2
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    multiply row three by

    -\frac{1}{3}

    Then use it to get the zero's above it.
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    multiply row three by

    -\frac{1}{3}

    Then use it to get the zero's above it.
    I still don't know where to go from here, still confused I've done row 3 divided by-1/3, but still can't figure it out
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by brumby_3 View Post
    I still don't know where to go from here, still confused I've done row 3 divided by-1/3, but still can't figure it out
    [1 0 5 | -1/2 -2 0]
    [0 1 -2| 1/2 1 0]
    [0 0 -3| 1 2 -1]

    \begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -3 & 1 & 2 & -1 \end{bmatrix}

    Now if you use

    -\frac{1}{3}R_3 \to R_3


    \begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & -\frac{1}{3} & \frac{2}{3} & -\frac{1}{3} \end{bmatrix}

    Now use the 1 in the to eliminate the the -2 and 5 above it
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  5. #5
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    Quote Originally Posted by TheEmptySet View Post
    [1 0 5 | -1/2 -2 0]
    [0 1 -2| 1/2 1 0]
    [0 0 -3| 1 2 -1]

    \begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -3 & 1 & 2 & -1 \end{bmatrix}

    Now if you use

    -\frac{1}{3}R_3 \to R_3

    \begin{bmatrix} 1 & 0 & 5 & -\frac{1}{2} & -2 & 0 \\ 0 & 1 & -2 & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & -\frac{1}{3} & \frac{2}{3} & -\frac{1}{3} \end{bmatrix}

    Now use the 1 in the to eliminate the the -2 and 5 above it
    According to the answer I'm given, the final matrix is:

    [9/2 -1 1]
    [-1 1 0]
    [-2 2 -1]

    How do you get that? If you've already figured out the bottom line to be [-1/3 2/3 -1/3]
    That's why I'm so confused, I can't get that answer.
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  6. #6
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Go back and double check your computations. You didn't post any work just where you were when you got stuck to I don't know where you went wrong.
    Personally I find it better to just start over and be really careful with your row operations.
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