Find A^-1 by adjoint method if A={{1, 2, - 2}, { - 1, 3, 0}, {1, - 2, 1}}
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Step-by-step explanation:
A=
⎣
⎢
⎢
⎡
1
0
1
0
2
2
1
3
1
⎦
⎥
⎥
⎤
∣A∣=1(2−6)−0(0−3)+1(0−2)
∣A∣=−4−2
∣A∣=−6
=0
∴A
−1
exists.
Minors Co-factors
M
11
=−4 A
11
=−4
M
12
=−3 A
12
=3
M
13
=−2 A
13
=−2
M
21
=−2 A
21
=2
M
22
=0 A
22
=0
M
23
=2 A
23
=−2
M
31
=−2 A
31
=−2
M
32
=3 A
32
=−3
M
33
=2 A
33
=2
adj(A)=
⎣
⎢
⎢
⎡
−4
3
−2
2
0
−2
−2
−3
2
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
1
⋅adj(A)
A
−0
=
6
−1
⎣
⎢
⎢
⎡
−4
3
−2
2
0
−2
−2
−3
2
⎦
⎥
⎥
⎤
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