what are we supposed to find in augmented matrix?

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You can augment a matrix with whatever you want. for example if you want to find the inverse of a matrix--       --|5 7 | 1 0||6 8 | 0 1|--       --and then manipulate the left side to an identity--                --|1 0 | -4.000 3.000||0 1 | 3.500 -2.500|--                --