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Question
Find the inverse of the following of the matrices , if it exists.
⎡⎢⎣223−32−2332⎤⎥⎦
⎡⎢⎣223−32−2332⎤⎥⎦
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Solution
⎡⎢⎣2−332233−22⎤⎥⎦A−1=⎡⎢⎣100010001⎤⎥⎦
R1↔R3
⎡⎢⎣3−222232−33⎤⎥⎦A−1=⎡⎢⎣001010100⎤⎥⎦
R1−R2
⎡⎢⎣1−4−12232−33⎤⎥⎦A−1=⎡⎢⎣0−11010100⎤⎥⎦
R2−2R1, R3−2R1
⎡⎢⎣1−4−10105055⎤⎥⎦A−1=⎡⎢⎣0−1103−212−2⎤⎥⎦
R2/10
⎡⎢⎣1−4−1011/2055⎤⎥⎦A−1=⎡⎢⎣0−1103/10−2/1012−2⎤⎥⎦
R1+4R2, R3−5R,
⎡⎢⎣101011/2005/2⎤⎥⎦A−1=⎡⎢⎣01/51/503/10−2/1011/2−1⎤⎥⎦
R3×25
⎡⎢⎣101011/2001⎤⎥⎦A−1=⎡⎢⎣01/51/503/10−2/102/51/5−2/5⎤⎥⎦
R1−R3,R2−12R3
⎡⎢⎣100010001⎤⎥⎦A−1=⎡⎢⎣−2/503/5−1/51/502/51/5−2/5⎤⎥⎦
A−1=15⎡⎢⎣−203−11021−2⎤⎥⎦
R1↔R3
⎡⎢⎣3−222232−33⎤⎥⎦A−1=⎡⎢⎣001010100⎤⎥⎦
R1−R2
⎡⎢⎣1−4−12232−33⎤⎥⎦A−1=⎡⎢⎣0−11010100⎤⎥⎦
R2−2R1, R3−2R1
⎡⎢⎣1−4−10105055⎤⎥⎦A−1=⎡⎢⎣0−1103−212−2⎤⎥⎦
R2/10
⎡⎢⎣1−4−1011/2055⎤⎥⎦A−1=⎡⎢⎣0−1103/10−2/1012−2⎤⎥⎦
R1+4R2, R3−5R,
⎡⎢⎣101011/2005/2⎤⎥⎦A−1=⎡⎢⎣01/51/503/10−2/1011/2−1⎤⎥⎦
R3×25
⎡⎢⎣101011/2001⎤⎥⎦A−1=⎡⎢⎣01/51/503/10−2/102/51/5−2/5⎤⎥⎦
R1−R3,R2−12R3
⎡⎢⎣100010001⎤⎥⎦A−1=⎡⎢⎣−2/503/5−1/51/502/51/5−2/5⎤⎥⎦
A−1=15⎡⎢⎣−203−11021−2⎤⎥⎦
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