Question

Q. Find A^-1 By using adjoint method
A= ​

Answer 1

Answer:

We have, A=[  

2

4

​

 

−2

3

​

]

Now, cofactor of A a  

11

​

=(−1)  

1+1

∣3∣

=3

a  

12

​

=(−1)  

1+2

∣4∣

=−4

a  

21

​

=(−1)  

2+1

∣−2∣

=2

a  

22

​

=(−1)  

2+2

∣2∣

=2

∴adj A=[  

3

2

​

 

−4

2

​

]

=[  

3

−4

​

 

2

2

​

]

Now, ∣A∣=[  

2

4

​

 

−2

3

​

]

=(2)(3)−(4)(−2)

=6+8

=14



=0

A is non-singular.

∴A  

−1

 exists A  

−1

=  

∣A∣

adj A

​

 

=  

14

1

​

[  

3

−4

​

 

2

2

​

]

=  

⎣

⎢

⎢

⎡

​

 

14

3

​

 

−  

14

4

​

 

​

 

14

2

​

 

14

2

​

 

​

 

⎦

⎥

⎥

⎤

​

=  

⎣

⎢

⎢

⎡

​

 

14

3

​

 

−  

7

2

​

 

​

 

7

1

​

 

7

1

​

 

​

 

⎦

⎥

⎥

⎤

​