1
Question
Find the inverse of the matrix A=⎡⎢⎣842294128⎤⎥⎦.
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Solution
⎛⎜⎝842294128⎞⎟⎠
=⎡⎢⎣842|100294|010128|001⎤⎥⎦
R2←R2−14⋅R1,R3←R3−18⋅R1
=⎡⎢
⎢
⎢
⎢
⎢⎣842|1000872|−1410032314|−1801⎤⎥
⎥
⎥
⎥
⎥⎦
R3←R3−316⋅R2
=⎡⎢
⎢
⎢
⎢
⎢⎣842|1000872|−14100022732|−564−3161⎤⎥
⎥
⎥
⎥
⎥⎦
R3←32227⋅R3,R2←R2−72⋅R3,R1←R1−2⋅R3
=⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣840|23222712227−64227080|−48227248227−112227001|−5454−622732227⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
R2←18⋅R2,R1←R1−4⋅R2
=⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣800|256227−112227−8227010|−622731227−14227001|−5454−622732227⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
R1←18⋅R1
=⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣100|32227−14227−1227010|−622731227−14227001|−5454−622732227⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
=⎛⎜
⎜
⎜
⎜
⎜
⎜
⎜⎝32227−14227−1227−622731227−14227−5454−622732227⎞⎟
⎟
⎟
⎟
⎟
⎟
⎟⎠
⎛⎜⎝842294128⎞⎟⎠
=⎡⎢⎣842|100294|010128|001⎤⎥⎦
R2←R2−14⋅R1,R3←R3−18⋅R1
=⎡⎢ ⎢ ⎢ ⎢ ⎢⎣842|1000872|−1410032314|−1801⎤⎥ ⎥ ⎥ ⎥ ⎥⎦
R3←R3−316⋅R2
=⎡⎢ ⎢ ⎢ ⎢ ⎢⎣842|1000872|−14100022732|−564−3161⎤⎥ ⎥ ⎥ ⎥ ⎥⎦
R3←32227⋅R3,R2←R2−72⋅R3,R1←R1−2⋅R3
=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣840|23222712227−64227080|−48227248227−112227001|−5454−622732227⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
R2←18⋅R2,R1←R1−4⋅R2
=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣800|256227−112227−8227010|−622731227−14227001|−5454−622732227⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
R1←18⋅R1
=⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣100|32227−14227−1227010|−622731227−14227001|−5454−622732227⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝32227−14227−1227−622731227−14227−5454−622732227⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠
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