Question

Find the characteristics equation of the following (1 2 0 2) , (2 1 1 2)

Answer 1

Answer:

Solution

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Correct option is

B

A  

3

−3A  

2

−I=O

So, A=  

⎣

⎢

⎢

⎡

​

 

1

1

2

​

 

1

2

1

​

 

0

1

0

​

 

⎦

⎥

⎥

⎤

​

 

Characteristics equation of matrix A is,

∣A−λI∣=0

⇒  

∣

∣

∣

∣

∣

∣

∣

∣

​

 

1−λ

1

2

​

 

1

2−λ

1

​

 

0

1

−λ

​

 

∣

∣

∣

∣

∣

∣

∣

∣

​

=0

⇒(1−λ)(−2λ+λ  

2

−1)−(−λ−2)=0

⇒−2λ+λ  

2

−1+2λ  

2

−λ  

3

+λ+λ+2=0

⇒−λ  

3

+3λ  

2

+1=0

⇒λ  

3

−2λ  

2

−1=0

As we know that, every matrix will satisfy its own characteistics equation

So, A  

3

−3A  

2

−I=O

Where, O denotes null matrix.

Step-by-step explanation: