adjoining matrix A ={6/2 5/1} is
Answers
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
12
=(−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
21
=(−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