find the inverse of A = 1 2 3
1 3 4
1 4 3
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Answer:
Step-by-step explanation:
Take A=AI
⎣
⎢
⎢
⎡
1
1
1
3
4
3
3
3
4
⎦
⎥
⎥
⎤
=A
⎣
⎢
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
c
2
→c
2
−3c
1
and c
3
→c
3
−3c
1
⎣
⎢
⎢
⎡
1
1
1
0
1
0
0
0
1
⎦
⎥
⎥
⎤
=A
⎣
⎢
⎢
⎡
1
0
0
−3
1
0
−3
0
1
⎦
⎥
⎥
⎤
c
1
→c
1
−c
2
⎣
⎢
⎢
⎡
1
0
1
0
1
0
0
0
1
⎦
⎥
⎥
⎤
=A
⎣
⎢
⎢
⎡
4
−1
0
−3
1
0
−3
0
1
⎦
⎥
⎥
⎤
c
1
→c
1
−c
3
⎣
⎢
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
=A
⎣
⎢
⎢
⎡
7
−1
−1
−3
0
0
−3
0
1
⎦
⎥
⎥
⎤
∴A
−1
=
⎣
⎢
⎢
⎡
7
−1
−1
−3
0
0
−3
0
1
⎦
⎥
⎥
⎤
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