# Toronto Math Forum

## MAT244-2013S => MAT244 Math--Tests => Term Test 2 => Topic started by: Matthew Cristoferi-Paolucci on March 27, 2013, 10:09:55 PM

Title: TT2 Question 1
Post by: Matthew Cristoferi-Paolucci 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*}
Title: Re: TT2 Question 1
Post by: Iven Poon on March 27, 2013, 10:24:27 PM
My super high quality solution for question 1.
Title: Re: TT2 Question 1
Post by: Victor Lam on March 28, 2013, 01:01:44 AM
my solution
Title: Re: TT2 Question 1
Post by: Victor Ivrii 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".
Title: Re: TT2 Question 1
Post by: Victor Lam 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.