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Math Help - Quick Question regarding Matrices.

  1. #1
    Junior Member Lonehwolf's Avatar
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    Quick Question regarding Matrices.

    Inverting and solving equations

    Code:
    1  -2  1
    3  1  2
    -1  4  1
    Find the inverse of that matrix, hence solve the following

    x-2y+z=1

    I have 2 more equations to solve, but I just need a quick rundown of the process

    To invert, I found the determinant (answer for it was -4 if anyone could confirm to see if I did the method right)

    I then took the transpose, and prcoeeded to complete that big 3x3 thing which involves taking the multiplication of diagonal "\" and add it to the multiplication of diagonal "/".

    The result of both the transpose and that process gave me this answer:

    Code:
    9 -6   5
    -1  0  -5
    11  -2  7
    What made me doubt everything was that the 3 equations given simply don't match up with either the inverse of the provided matrix, with the matrix itself, or anything similar that I can recall.

    Any help on this would be much appreciated.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Lonehwolf View Post
    Inverting and solving equations

    Code:
    1  -2  1
    3  1  2
    -1  4  1
    Find the inverse of that matrix, hence solve the following

    x-2y+z=1

    I have 2 more equations to solve, but I just need a quick rundown of the process

    To invert, I found the determinant (answer for it was -4 if anyone could confirm to see if I did the method right)

    I then took the transpose, and prcoeeded to complete that big 3x3 thing which involves taking the multiplication of diagonal "\" and add it to the multiplication of diagonal "/".

    The result of both the transpose and that process gave me this answer:

    Code:
    9 -6   5
    -1  0  -5
    11  -2  7
    What made me doubt everything was that the 3 equations given simply don't match up with either the inverse of the provided matrix, with the matrix itself, or anything similar that I can recall.

    Any help on this would be much appreciated.
    Actually the one equation you do happen to give does match with the given coeffcient matrix, and I'm sure the other two equations do to.

    I hope you realise that to solve AX = B you do the following: A^{-1} A X = A^{-1} B \Rightarrow X = A^{-1} B.

    Your inverse is wrong. And the determinant is 16, not -4.

    I rather like the method for finding the inverse that is explained so well here: Matrix Inversion: Finding the Inverse of a Matrix
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  3. #3
    Junior Member Lonehwolf's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Actually the one equation you do happen to give does match with the given coeffcient matrix, and I'm sure the other two equations do to.

    I hope you realise that to solve AX = B you do the following: A^{-1} A X = A^{-1} B \Rightarrow X = A^{-1} B.

    Your inverse is wrong. And the determinant is 16, not -4.

    I rather like the method for finding the inverse that is explained so well here: Matrix Inversion: Finding the Inverse of a Matrix

    Thanks, go the determinant right finally.

    Regarding matching the equation with the coefficient matrix - I can't figure that one out. Which line has specifically matched?

    Reworking the transpose and that big square thingy I ended up with a different result:
    Code:
    9 -2  -3
    -1 0  -5
    11 -6 -5
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  4. #4
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    Quote Originally Posted by Lonehwolf View Post
    Thanks, go the determinant right finally.

    Regarding matching the equation with the coefficient matrix - I can't figure that one out. Which line has specifically matched?

    Reworking the transpose and that big square thingy I ended up with a different result:
    Code:
    9 -2  -3
    -1 0  -5
    11 -6 -5
    Look at the coeeficients of the first equation and look at the first line of your coefficient matrix ....

    Your inverse is still wrong. You only have to multiply the two matrices together to quickly see this ....
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