EigenVectors

[Frogger888]

Okay I got most of the problem I just need help with the last step
I found 3 eigen values which are: 2,2,2

i) eigenvalue=2 Matrix (0 -1 0 | 0 )
(5 0 4 | 0 )
(0 1 0 | 0 )
for my 1st eigenvector I get ( -1 )
( 0 )
(-5/4 )
How do I get two more eigenvectors for the other 2 eigen values which are 2, 2

Thanks

 

[pka]

There appears to be a mistake in your question.
What is the actual matrix involved?
Please state the entire question.

 

[Frogger888]

The actual matrix is: Find the eigenvalues and eigenvectors

2 -1 0
5 2 4
0 1 2

So next I took the determinant of that which gave me

(2-x)(2-x)(2-x)4=0

this gave me eigen values of 2, 2, and 2

next matrix is for eigen value:2 is
i)

0 -1 0 | 0
5 0 4 | 0
0 1 0 | 0

 

[pka]

Given this matrix \(\displaystyle M = \left[ {\begin{array}{c}
2 & { - 1} & 0 \\
5 & 2 & 4 \\
0 & 1 & 2 \\
\end{array}} \right]\)

I get different Eigenvalues: \(\displaystyle \left| {xI(3) - M} \right| = x^3 - 6x^2 + 13x - 10\quad \Rightarrow \quad x \in \{ 2,2 + i,2 - i\}\)

 

[Frogger888]

Let me recheck my work and see what I get
I will reply in a little bit

 

[Frogger888]

Okay here we go I get for eigenvalue 2+i the matrix

-i -1 0 | 0
5 -i 4 | 0
0 1 -i | 0

from this I get the values

-iksub3
4ksub3-i5ksub3
iksub3

then I get for 2 of the eigenvectors These should have matrixes around them

0 -i 0 -i
4 - -5i 4 + -5
0 i 0 i

 

[Frogger888]

That last part did not come out right


0 -i
4 - -5i
0 i

then for the next one just change the sign to +