# Quick Eigenvectors Question

• Oct 17th 2011, 01:36 AM
Paymemoney
Quick Eigenvectors Question
Hi
The following question ask to find eigenvector:

$\left[ \begin{matrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 1 \end{matrix} \right]$

Now the answer i got was correct according to book, however i don't understand why they choose these two values instead of the other one, which is the repeated eigenvalue 1:

eigenvalue 5
$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

eigenvalue 1 repeated value
$\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right]$

$\left[ \begin{matrix} -1 \\ 1 \\ 0 \end{matrix} \right]$

$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

P.S
• Oct 17th 2011, 01:48 AM
alexmahone
Re: Quick Eigenvectors Question
Quote:

Originally Posted by Paymemoney
Hi
The following question ask to find eigenvector:

$\left[ \begin{matrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 1 \end{matrix} \right]$

Now the answer i got was correct according to book, however i don't understand why they choose these two values instead of the other one, which is the repeated eigenvalue 1:

eigenvalue 5
$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

eigenvalue 1 repeated value
$\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right]$

$\left[ \begin{matrix} -1 \\ 1 \\ 0 \end{matrix} \right]$

$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

P.S

Let $A=\left[ \begin{matrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 1 \end{matrix} \right]$.

$A\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]=5\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

$A\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right]=1\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right]$

$A\left[ \begin{matrix} -1 \\ 1 \\ 0 \end{matrix} \right]=1\left[ \begin{matrix} -1 \\ 1 \\ 0 \end{matrix} \right]$
• Oct 17th 2011, 03:12 AM
Paymemoney
Re: Quick Eigenvectors Question
maybe my question is not clear. Is $\left [ \begin{matrix} 1 \\ 1 \\ 0 \\ \end{matrix} \right ]$ an acceptable answer?
• Oct 17th 2011, 03:59 AM
Deveno
Re: Quick Eigenvectors Question
is (1,1,0) an eigenvector? yes, corresponding to the eigenvalue 5 (see post #2).
• Oct 17th 2011, 08:25 AM
HallsofIvy
Re: Quick Eigenvectors Question
Quote:

Originally Posted by Paymemoney
Hi
The following question ask to find eigenvector:

$\left[ \begin{matrix} 3 & 2 & 0 \\ 2 & 3 & 0 \\ 0 & 0 & 1 \end{matrix} \right]$

Now the answer i got was correct according to book, however i don't understand why they choose these two values instead of the other one, which is the repeated eigenvalue 1:

eigenvalue 5
$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$

eigenvalue 1 repeated value
$\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right]$

$\left[ \begin{matrix} -1 \\ 1 \\ 0 \end{matrix} \right]$

$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$
$\left[ \begin{matrix} 1 \\ 1 \\ 0 \end{matrix} \right]$