Toronto Math Forum
MAT2442013S => MAT244 MathTests => Term Test 2 => Topic started by: Matthew CristoferiPaolucci 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*}

My super high quality solution for question 1.

my solution

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".

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.