Question

Anyone good at Eigen Vectors.

Answer 1

im good at eigen values

Answer 2

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.

Answer 3

do you have your eigen values ?

Answer 4

yes i have .. its 2

Answer 5

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)...

Answer 6

Where is lambda??
Oh my God...

Answer 7

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

Answer 8

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...

Answer 9

i have found lammida.. and its 2

Answer 10

there is repeated roots?

Answer 11

yes all 3 values of lamida are 2

Answer 12

I try to find eigen value now...

You can carry on @UnkleRhaukus

Answer 13

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

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

Answer 14

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

Answer 15

ok.. got this far...

Answer 16

you have three simultaneous equations

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

\[4x_1 + 5x_2 + 2x_3 = 0\]
\[2x_1 -2x_2 - 8x_3 = 0\]
\[5x_1 + 4x_2 - 2x_3 = 0\]

Answer 21

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

Answer 22

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

Answer 23

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