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I have got some enquires for eigenvalue and eigenvector.

Consider the 1st matrix:

A = [ 1 2 3]

[ 0 5 6]

[ 0 6 5]

The characteristic polynomial is

det(A-λI) = [ 1-λ 2 3]

[ 0 5-λ 6]

[ 0 6 5-λ]

= (1-λ) [ (5-λ)^2 - 36]

The eigenvaules are D(λ) = 0 ---> λ1 = 1, λ2=-1 and λ3 =11

May i know how do we get the λ1 , λ2 and λ3? Can someone advise me?

Dont seem quadratic is working for this??

Matrix (2)

A = [3 5 3]

[0 4 6]

[0 0 1]

Is the characteristic polynomial: det(A - λI) = [ 3-λ 5 3]

[ 0 4-λ 6]

[ 0 0 1-λ]

= (3-λ)[(4-λ)(1-λ)- 0]?

Does the characteristic polynomial of matrix 2 also the same as Matrix (3)

A = [ 3 0 0]

[ 4 4 0]

[ 5 6 1]

Please advise. Thanks :)