### Author Topic: TT2 Question 1  (Read 6158 times)

#### Matthew Cristoferi-Paolucci

• Jr. Member
• Posts: 10
• Karma: 8
##### TT2 Question 1
« on: March 27, 2013, 10:09:55 PM »
\begin{equation*}
\left\{ \begin{array}{ll}
x'=-3y+7z\\
y'=-y+5z\\
z'=-y+z
\end{array}\right.
\end{equation*}
« Last Edit: March 27, 2013, 10:16:40 PM by Victor Ivrii »

#### Iven Poon

• Newbie
• Posts: 4
• Karma: 2
##### Re: TT2 Question 1
« Reply #1 on: March 27, 2013, 10:24:27 PM »
My super high quality solution for question 1.
« Last Edit: March 27, 2013, 10:41:06 PM by Iven Poon »

#### Victor Lam

• Jr. Member
• Posts: 13
• Karma: 9
##### Re: TT2 Question 1
« Reply #2 on: March 28, 2013, 01:01:44 AM »
my solution

#### Victor Ivrii

• Elder Member
• Posts: 2607
• Karma: 0
##### Re: TT2 Question 1
« Reply #3 on: March 28, 2013, 03:03:50 AM »
Matthew' solution is correct but in some way incomplete: since two eigenvalues are complex (and complex conjugate) there are two forms of solutions: a complex form and he found only the complex form; Iven and Victor found both. despite Victor' solution looks different it is not: in fact he got the same eigenvector albeit multiplied by factor $-2i$ (which be also an eigenvector) and this is the source of "discrepancy".

#### Victor Lam

• Jr. Member
• Posts: 13
• Karma: 9
##### Re: TT2 Question 1
« Reply #4 on: March 28, 2013, 04:35:02 PM »
It appears that I have left out a negative sign in my previous scan. My apologies. For completion, I have fixed the error in red in the re scan.