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## nubeer 3 years ago Anyone good at Eigen Vectors.

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1. UnkleRhaukus

im good at eigen values

2. nubeer

ohh finally.. ok i have a question.. i know how to solve.. just for oncae type of case i dont know how to solve.. i will post up the question [ 6 5 2 2 0 -8 5 4 0 ] this is the matrix.

3. zzr0ck3r

do you have your eigen values ?

4. nubeer

yes i have .. its 2

5. waterineyes

If I am not getting it wrong, then I think we will do like this to find eigen values : A - IX = 0 Something like that... No knowledge... @UnkleRhaukus please help your friend (me)...

6. waterineyes

Where is lambda?? Oh my God...

7. UnkleRhaukus

$\textbf Ax=\lambda x$$(\textbf A-\lambda \textbf I)x=0$

8. waterineyes

Oh yeah.... I forgot all the things... One day, I found a page thrown by someone on the road, I read that.. There on the page, it was shown how to find Eigen values but the question was not complete.. And I have forgot that too...

9. nubeer

i have found lammida.. and its 2

10. UnkleRhaukus

there is repeated roots?

11. nubeer

yes all 3 values of lamida are 2

12. waterineyes

I try to find eigen value now... You can carry on @UnkleRhaukus

13. UnkleRhaukus

$\textbf A=\left[\begin{array}{ccc}6&5&2\\2&0&-8\\5&4&0\end{array}\right]$$x=\left[\begin{array}{ccc} x_1\\x_2\\x_3\end{array}\right]$$\lambda=2$ $\left[\begin{array}{ccc}6&5&2\\2&0&-8\\5&4&0\end{array}\right]\left[\begin{array}{ccc} x_1\\x_2\\x_3\end{array}\right]=2\left[\begin{array}{ccc} x_1\\x_2\\x_3\end{array}\right]$

14. UnkleRhaukus

$\left[\begin{array}{ccc}6-2&5&2\\2&0-2&-8\\5&4&0-2\end{array}\right]\left[\begin{array}{ccc} x_1\\x_2\\x_3\end{array}\right]=\left[\begin{array}{ccc} 0\\0\\0\end{array}\right]$

15. nubeer

ok.. got this far...

16. UnkleRhaukus

you have three simultaneous equations

17. nubeer

ok so i have to just solve simultaneously to get first eigen vector?

18. UnkleRhaukus

something like that, i always go confused when it comes to eigenvectors

19. nubeer

i think first eigen vector is x1= = 2 x2 = -2 x3 = 1

20. waterineyes

$4x_1 + 5x_2 + 2x_3 = 0$ $2x_1 -2x_2 - 8x_3 = 0$ $5x_1 + 4x_2 - 2x_3 = 0$

21. UnkleRhaukus

@nubeer , that certainly solves the three equations, how did you get there?

22. nubeer

i have found x1 and x2 in terms of x3 while using subsitution method.

23. nubeer

ok thanks guys.. i think i have done it... thank you very much espacially @UnkleRhaukus :)

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