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Adjoining matrix A ={6/2 5/1} is |
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Answer» ong>Answer: Let A= ⎣ ⎢ ⎢ ⎡
1 2 2
1 3 0
2 5 1
⎦ ⎥ ⎥ ⎤
We know that adjA=C T
So, we will find out co-factors of each element of A. C 11
=(−1) 1+1
∣ ∣ ∣ ∣ ∣ ∣
3 0
5 1
∣ ∣ ∣ ∣ ∣ ∣
⇒C 11
=3−0=3 C
=(−1) 1+2
∣ ∣ ∣ ∣ ∣ ∣
2 2
5 1
∣ ∣ ∣ ∣ ∣ ∣
⇒C 12
=−(2−10)=8 C 13
=(−1) 1+3
∣ ∣ ∣ ∣ ∣ ∣
2 2
3 0
∣ ∣ ∣ ∣ ∣ ∣
⇒C 13
=0−6=−6 C
=(−1) 2+1
∣ ∣ ∣ ∣ ∣ ∣
1 0
2 1
∣ ∣ ∣ ∣ ∣ ∣
⇒C 21
=−(1−0)=−1 C 22
=(−1) 2+2
∣ ∣ ∣ ∣ ∣ ∣
1 2
2 1
∣ ∣ ∣ ∣ ∣ ∣
⇒C 22
=1−4=−3 C 23
=(−1) 2+3
∣ ∣ ∣ ∣ ∣ ∣
1 2
1 0
∣ ∣ ∣ ∣ ∣ ∣
⇒C 23
=−(0−2)=2 C 31
=(−1) 3+1
∣ ∣ ∣ ∣ ∣ ∣
1 3
2 5
∣ ∣ ∣ ∣ ∣ ∣
⇒C 31
=5−6=−1 C 32
=(−1) 3+2
∣ ∣ ∣ ∣ ∣ ∣
1 2
2 5
∣ ∣ ∣ ∣ ∣ ∣
⇒C 32
=−(5−4)=−1 C 33
=(−1) 3+3
∣ ∣ ∣ ∣ ∣ ∣
1 2
1 3
∣ ∣ ∣ ∣ ∣ ∣
⇒C 33
=3−2=1 So, the cofactor MATRIX C= ⎣ ⎢ ⎢ ⎡
3 −1 −1
8 −3 −1
−6 2 1
⎦ ⎥ ⎥ ⎤
⇒C T = ⎣ ⎢ ⎢ ⎡
3 8 −6
−1 −3 2
−1 −1 1
⎦ ⎥ ⎥ ⎤
Hence, adjA= ⎣ ⎢ ⎢ ⎡
3 8 −6
−1 −3 2
−1 −1 1
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