Question

find the eogen value and eigen vector of the matrix
8 -6 2
-6 7 -4
2 -4 3​

Answer 1

Answer:

Please find the attached file.

Step-by-step explanation:

Answer 2

In straight variable-based math, an eigenvector or trademark vector of a direct change is a nonzero vector that changes all things considered by a scalar component when that straight change is applied to it.

The comparing eigenvalue, regularly meant by \lambda, is the element by which the eigenvector is scaled.

|A-λI|=0

(8-λ)           -6         2

-6       (7-λ)        -4

2          -4       (3-λ)

|=0

(8-λ)((7-λ)×(3-λ)-(-4)×(-4))-(-6)((-6)×(3-λ)-(-4)×2)+2((-6)×(-4)-(7-λ)×2)=0

(8-λ)((21-10λ+λ2)-16)+6((-18+6λ)-(-8))+2(24-(14-2λ))=0

(8-λ)(5-10λ+λ2)+6(-10+6λ)+2(10+2λ)=0

(40-85λ+18λ2-λ3)+(-60+36λ)+(20+4λ)=0

(-λ3+18λ2-45λ)=0

-λ(λ-3)(λ-15)=0

∴ the eigenvalues of the matrix A are given by λ=0,3,15