Find eigenvalues and eigenvector

Re: Find eigenvalues and eigenvector

your determinant does not look correct. i get you should have:

(λ-3)(λ)(λ+1) + (1)(-5)(-4) + (1)(12)(2) - (-4)(λ)(1) - (-5)(2)(λ-3) - (λ+1)(1)(12)

= λ^3 - 2λ^2 - 3λ + 20 + 24 + 4λ + 10λ - 30 - 12λ - 12

= λ^3 - 2λ^2 - λ + 2

Re: Find eigenvalues and eigenvector

Re: Find eigenvalues and eigenvector

λ=2: (λI-A)=0

[(-1,1,1), (12,2,-5), (-4,2,3)] [x1, x2, x3] = 0

-x1 + x2 + x3 = 0

x1 = 2

x2 = 1

x3 = 1

λ=1: (λI-A)=0

[(-2, 1, 1), (12, 1, -5), (-4, 2, 2)] [x1, x2, x3] = 0

-2x1 + x2 + x3 = 0

x1 = 1

x2 = 1

x3 = 1

λ=-1: (λI-A)=0

[(-4, 1, 1), (12, -1, -5), (-4, 2, 0)] [x1. x2. x3] = 0

-4x1 + x2 + x3 = 0

x1 = 1

x2 = 2

x3 = 2

Are these eigenvector correct?

Re: Find eigenvalues and eigenvector

I alos need help on finding the eigenvector and want some clarity.

Are you suppose to just multiply the 3x3 and the 3x1 matrix to get a 3x1 matrix or are you suppose to take the parametric vector form?

Also shouldn't the solution be (x1, y1, z1)^T?

ANd what is x1, y1, and z1? Are they our respective eigenvalues?

And what do you do when there is a repeated eigenvalue? Does that mean there will be two of the same eigenvectors?