Question

Eigensvectors and eigensvalue.

Answer 1

who Eigen?

Answer 2

jk:P

Answer 3

I have this matrix
\[A=\left[\begin{matrix}1 & 2&3 \\ 2 & 4&6\\3&6&9\end{matrix}\right]\]
and I need to show that A has the following tree vectors as eigenvectors. In addition to this I have to find the tree eigenvalues.

Answer 4

do you know how to find Eigen values?

Answer 5

you want these first

Answer 6

\[v1=\left(\begin{matrix}-2 \\ 1 \\ 0\end{matrix}\right)\]
\[v2=\left(\begin{matrix}1 \\ 2 \\ 3\end{matrix}\right)\]
\[v3=\left(\begin{matrix}3 \\ 6 \\ -5\end{matrix}\right)\]

Answer 7

Yes i know have to find the eigenvalues.

Answer 8

ok can you give me the latek code you for the matrix to save time...:)

Answer 9

\[\begin{matrix}1-a & 2&3 \\ 2 & 4-b&6\\3&6&9-c\end{matrix}\]

Answer 10

The task says that I must first show that these three are the eigen vector.

Answer 11

and then find the eigenvalues.

Answer 12

ok well you need the Eigen values first
Av=ev
where e is Eigen values and v is Eigen vectors

Answer 13

maybe anther way sec..

Answer 14

\[Av=\lambda v\]

Answer 15

yeah ok, so do Av and it will equal v times a constant

Answer 16

So I can do it like this?

Answer 17

where are you getting [14,28,42]?

Answer 18

on the first one
av = 0

Answer 19

Sorry

Answer 20

out side of that, yes

Answer 21

yep

Answer 22

those constants are your eigenvalues

Answer 23

so its pretty easy to get the values if you have the vectors, but I don't know of a non guess and check method of getting the vectors without the values...

Answer 24

that's prob next in your class...

Answer 25

So that is enough.

Answer 26

yep you found a three vectors such that your matrix times that vector is equal to a constant times that vector

Answer 27

so you reduced your matrix to a constant:)

Answer 28

Thanks..

Answer 29

np