Question

find all the eigenvalues and eigenvsctors of A=[-2-11-12-11-12]

Answer 1

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

Step-by-step explanation:

pls mark me as Braineliest