the eigen values of a matrix A are 2,3,1 then find the eigen values of A^-1 + A^2
Answers
Answered by
4
Answer:
A=
⎣
⎢
⎢
⎡
2
2
−1
1
3
−1
1
4
−2
⎦
⎥
⎥
⎤
∣A−λI∣=0
⎣
⎢
⎢
⎡
2−λ
2
−1
1
3−λ
−1
1
4
−2−λ
⎦
⎥
⎥
⎤
=0
(2−λ)[(3−λ)(−2−λ)+4]−1[−4−2λ+4]+[−2+3−λ]=0
(2−λ)[λ
2
−λ−2]+λ+1=0
−λ
3
+3λ
2
+λ−3=0
λ
3
−3λ
2
−λ+3=0
(λ−1)(λ
2
−2λ−3)=0
(λ−1)(λ+1)(λ−3)=0
λ=−1,1,3
Therefore, Eigen values of matrix A are −1,1,3
Answered by
4
Answer:
The eigen values of is 4.5, 9.33, 2.
Step-by-step explanation:
Tip:
- According to Cayley Hamilton theorem, every square matrix satisfies its Characteristic equation.
- Putting the values of eigen value at place of A we can get Eigen values of
Step1 of 1:
- Put A =2, then Eigen value is
- Put A =3 , then Eigen value is
- Put A =1, then Eigen value is
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