# Toronto Math Forum

## MAT244-2013F => MAT244 Math--Tests => Quiz 5 => Topic started by: Victor Ivrii on November 20, 2013, 08:40:10 PM

Title: Problem 2, night sections
Post by: Victor Ivrii on November 20, 2013, 08:40:10 PM
Express the general solution of the given system of equations in terms of real-valued functions.
\begin{equation*}
\mathbf{x}'=\begin{pmatrix}2 &-5\\1 &-2\end{pmatrix}\mathbf{x}.
\end{equation*}
Title: Re: Problem 2, night sections
Post by: Yangming Cai on November 20, 2013, 09:30:32 PM
Title: Re: Problem 2, night sections
Post by: Victor Ivrii on November 21, 2013, 05:13:08 AM
Title: Re: Problem 2, night sections
Post by: Yangming Cai on November 21, 2013, 12:18:29 PM
\begin{array}{l}\det (A - rI) = \left( {\begin{array}{*{20}{c}}{2 - r}&{ - 5}\\1&{ - 2 - r}\end{array}} \right) = {r^2} + 1 = 0\\r =  \pm i\\{\rm{when }} r = i\\(2 - i){\xi _1} = 5{\xi _2}{\rm{   and }}{\xi ^1} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right)\\{x^1} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right){e^{it}} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right)(\cos t + i\sin t)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \left( {\begin{array}{*{20}{c}}{5\cos t}\\{2\cos t + \sin t}\end{array}} \right) + i\left( {\begin{array}{*{20}{c}}{5\sin t}\\{2\sin t - \cos t}\end{array}} \right)\\x = {c_1}\left( {\begin{array}{*{20}{c}}{5\cos t}\\{2\cos t + \sin t}\end{array}} \right) + {c_2}\left( {\begin{array}{*{20}{c}}{5\sin t}\\{2\sin t - \cos t}\end{array}} \right)\end{array}
Title: Re: Problem 2, night sections
Post by: Victor Ivrii on November 21, 2013, 05:35:54 PM
Again, what crapware produce this code?

Code: [Select]
\begin{array}{l}\det (A - rI) = \left( {\begin{array}{*{20}{c}}{2 - r}&{ - 5}\\1&{ - 2 - r}\end{array}} \right) = {r^2} + 1 = 0\\r =  \pm i\\{\rm{when }} r = i\\(2 - i){\xi _1} = 5{\xi _2}{\rm{   and }}{\xi ^1} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right)\\{x^1} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right){e^{it}} = \left( {\begin{array}{*{20}{c}}5\\{2 - i}\end{array}} \right)(\cos t + i\sin t)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \left( {\begin{array}{*{20}{c}}{5\cos t}\\{2\cos t + \sin t}\end{array}} \right) + i\left( {\begin{array}{*{20}{c}}{5\sin t}\\{2\sin t - \cos t}\end{array}} \right)\\x = {c_1}\left( {\begin{array}{*{20}{c}}{5\cos t}\\{2\cos t + \sin t}\end{array}} \right) + {c_2}\left( {\begin{array}{*{20}{c}}{5\sin t}\\{2\sin t - \cos t}\end{array}} \right)\end{array}
Title: Re: Problem 2, night sections
Post by: Yangming Cai on November 21, 2013, 06:59:10 PM
I used mathtype in word, is there anything wrong with this s.w?
Title: Re: Problem 2, night sections
Post by: Victor Ivrii on November 22, 2013, 09:03:23 AM
I used mathtype in word, is there anything wrong with this s.w?

You definitely used it incorrectly--to type everything, not only math snippets. However I have seen a correct usage of it--and the source is ugly, contains tons of unnecessary elements,  and it is very difficult to edit it by hand later or reuse it.