Eigenvalues and eigenvectors?

Question

expand the determinant of

[2-λ 8 10

8 4-λ 5

10 5 7-λ]

and solve for the eigenvalues and their corresponding eigenvectors.

Answer 1

Do your own homework.

Answer 2

getting the determinant:

(2-λ)(4-λ)(7-λ) + 8*5*10 + 10*8*5 - (4-λ)10*10 - (2-λ)5*5 - (7-λ)8*8

= -λ^3 + 13λ^2 + 139λ - 42

=-(λ - 19.8842)(λ + 7.17848)(λ - 0.294244) .. . . it turns out the roots are irrational

λ = 19.884236027

x = 0.90351093108

y = 0.76982534306

z = 1

.. . .. .

λ = -7.1784802015

x = -1.859639596

y = 0.88358315174

z = 1

.. . .. .

λ = 0.29424417486

x = -0.051014192238

y = -1.2391227806

z = 1