Toronto Math Forum
MAT244-2013F => MAT244 Math--Tests => Quiz 5 => Topic started by: Victor Ivrii on November 20, 2013, 08:40:10 PM
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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*}
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answer as follow
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Difficult to read.
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\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}
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Again, what crapware produce this code?
\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}
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I used mathtype in word, is there anything wrong with this s.w?
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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.