### Author Topic: Problem 2, night sections  (Read 6196 times)

#### Victor Ivrii

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##### Problem 2, night sections
« 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*}

#### Yangming Cai

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##### Re: Problem 2, night sections
« Reply #1 on: November 20, 2013, 09:30:32 PM »
answer as follow

#### Victor Ivrii

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##### Re: Problem 2, night sections
« Reply #2 on: November 21, 2013, 05:13:08 AM »
Difficult to read.

#### Yangming Cai

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##### Re: Problem 2, night sections
« Reply #3 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}
« Last Edit: November 21, 2013, 12:54:19 PM by Yangming Cai »

#### Victor Ivrii

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##### Re: Problem 2, night sections
« Reply #4 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}

#### Yangming Cai

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##### Re: Problem 2, night sections
« Reply #5 on: November 21, 2013, 06:59:10 PM »
I used mathtype in word, is there anything wrong with this s.w?

#### Victor Ivrii

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##### Re: Problem 2, night sections
« Reply #6 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.