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Hi,

I am trying to find the eigenvectors for the following 3x3 matrix and are having trouble with it. The matrix is

(I have a ; since I can't have a space between each column. Sorry):

[20 ; -10 ; 0]

[-10 ; 30 ; 0]

[0 ; 0 ; 40]

I’ve already calculated the eigenvalues, which are: λ1=13.8196, λ2=36.18 , λ3= 40

The next step is to calculate the eigenvectors for every eigenvalue λ and it’s now I keep getting the wrong answer. Let us take λ1 for instance. We'll get:

[20-13.8192 ; -10 ; 0]

[-10 ; 30-13.8196 ; 0]

[0 ; 0 ; 40-13.8196]

According to the solution manual, we get the following eigenvector for the eigenvalue λ1 :

[ 0.85066 ]

[ 0.527 ]

[ 0 ]

I tried to reduce the matrix by following these steps:

[20-13.8192 ; -10 ; 0] [6.1808 ; -10 ; 0] [1 ; -1.6179 ; 0]

[-10 ;30-13.8196 ; 0] ~ [-10 ; -16.1808 ; 0] ~ [-1 ; 1.6181 ; 0]

[0 ; 0 ; 40-13.8196] [0 ; 0 ; 1] [0 ; 0 ; 0]

I don’t get anywhere after this since, as can be seen, I won't get the same eigenvectors. How did they get 0.85066 and 0.527 ?! If you can explain it for λ1 then I'll probably solve it for λ2 and λ3 as well.

Thanks!

I am trying to find the eigenvectors for the following 3x3 matrix and are having trouble with it. The matrix is

(I have a ; since I can't have a space between each column. Sorry):

[20 ; -10 ; 0]

[-10 ; 30 ; 0]

[0 ; 0 ; 40]

I’ve already calculated the eigenvalues, which are: λ1=13.8196, λ2=36.18 , λ3= 40

The next step is to calculate the eigenvectors for every eigenvalue λ and it’s now I keep getting the wrong answer. Let us take λ1 for instance. We'll get:

[20-13.8192 ; -10 ; 0]

[-10 ; 30-13.8196 ; 0]

[0 ; 0 ; 40-13.8196]

According to the solution manual, we get the following eigenvector for the eigenvalue λ1 :

[ 0.85066 ]

[ 0.527 ]

[ 0 ]

I tried to reduce the matrix by following these steps:

[20-13.8192 ; -10 ; 0] [6.1808 ; -10 ; 0] [1 ; -1.6179 ; 0]

[-10 ;30-13.8196 ; 0] ~ [-10 ; -16.1808 ; 0] ~ [-1 ; 1.6181 ; 0]

[0 ; 0 ; 40-13.8196] [0 ; 0 ; 1] [0 ; 0 ; 0]

I don’t get anywhere after this since, as can be seen, I won't get the same eigenvectors. How did they get 0.85066 and 0.527 ?! If you can explain it for λ1 then I'll probably solve it for λ2 and λ3 as well.

Thanks!