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    How would i find an inverse of a matrix using row reduction?

    Its really confusing me, and my lecturer is terrible, she didnt really explain.

    I understand that it needs to have a zero determinant, but i dont understand the method.

    For example if i had the matrix
    (a b c)
    (d e f)
    (g h i)

    (sorry i dont know how to write matrices on computers... that is all one matrix)

    Thanks for all the help, i just need to know the method
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    Augment your matrix with the identity matrix, which basically means "stick them together", like this:

    \left(\begin{array}{c c c|c c c} a&b&c&1&0&0 \\ d&e&f&0&1&0 \\ g&h&i&0&0&1 \end{array}\right)

    and then perform row operations on the whole 3*6 matrix. (Ignore the vertical line for this purpose - it doesn't do anything special, it just serves as a convenient reminder of where your original matrix was and where the identity matrix was.) Your aim is to use row operations to turn the bit to the left of the vertical line into the identity matrix; once you've done that, the bit to the right of the vertical line will be the inverse of your original matrix.
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    (Original post by generalebriety)
    Augment your matrix with the identity matrix, which basically means "stick them together", like this:

    \left(\begin{array}{c c c|c c c} a&b&c&1&0&0 \\ d&e&f&0&1&0 \\ g&h&i&0&0&1 \end{array}\right)

    and then perform row operations on the whole 3*6 matrix. (Ignore the vertical line for this purpose - it doesn't do anything special, it just serves as a convenient reminder of where your original matrix was and where the identity matrix was.) Your aim is to use row operations to turn the bit to the left of the vertical line into the identity matrix; once you've done that, the bit to the right of the vertical line will be the inverse of your original matrix.
    Okay i think i understand a bit better. How do i use row operation to do that though? I change the matrix on the right to the matrix on the left?
    Sorry i really dont understand matrices.
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    (Original post by ponpon14)
    Okay i think i understand a bit better. How do i use row operation to do that though? I change the matrix on the right to the matrix on the left?
    Sorry i really dont understand matrices.
    No, you ignore the matrix on the right. Use row operations on the whole matrix, but only concentrate on the matrix on the left (the matrix on the right will secretly keep track of things without you paying too much attention to it), and changing the matrix on the left into the identity. (Do you understand how you use row operations? If I told you to forget about augmenting the matrix and just use row operations to change your original matrix into the identity, would you know how?)
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    http://math.uww.edu/~mcfarlat/inverse.htm

    This site shows a worked example for the method that generalebriety just described.
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    Okay, yeah thats making a bit more sense. Il do some practice now and see where i get Thanks
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    Edit: Sorry, never mind. Ive figured it out after a very silly moment!!!
 
 
 
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