Toronto Math Forum
MAT2442013F => MAT244 MathTests => Quiz 5 => Topic started by: Victor Ivrii on November 20, 2013, 08:40:10 PM

Express the general solution of the given system of equations in terms of realvalued functions.
\begin{equation*}
\mathbf{x}'=\begin{pmatrix}2 &5\\1 &2\end{pmatrix}\mathbf{x}.
\end{equation*}

answer as follow

Difficult to read.

\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}

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}

I used mathtype in word, is there anything wrong with this s.w?

I used mathtype in word, is there anything wrong with this s.w?
You definitely used it incorrectlyto type everything, not only math snippets. However I have seen a correct usage of itand the source is ugly, contains tons of unnecessary elements, and it is very difficult to edit it by hand later or reuse it.