Question

1) Find the characteristic equation of the matrix
A= 2 2 1
1 3 1
1 2 2 and hence determined in inverse​

Answer 1

Answer:

Characteristic equation is

|A−λI|=0⇒[2−λ312−λ]=0

⇒(2−λ)2−3=0

⇒λ2−4λ+1=0

Step-by-step explanation:

therefore Cayley-hamiltion theorem,

A2−4A+I=OorI=4A−A2

Multiplying byA−1, we get

A−1=4A−1A−A−1AA

=4I−IA=4I−A

=4[1001]−{2312]

[2−3−12]

Thanks please like if it was helpful

Nice question