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lines changed Original file line number Diff line number Diff line change @@ -3032,9 +3032,8 @@ \section{Solutions to Chapter Problems}
303230320&1 + t + {{t^2}\over {2}} + {{t^3}\over {3!}} + \cdots\cr
30333033}\right ] \\
30343034&=&\left [\matrix {
3035- e^t&
3036- te^t\cr
3037- 0&e^t\cr
3035+ e^t & t e^t\cr
3036+ 0 & e^t\cr
30383037}\right ]
30393038\end {eqnarray* }
30403039\item [d,e)] We are looking for all matrices that satisfy $ B^2 =A$ . Let
@@ -4068,4 +4067,4 @@ \section{Solutions to Chapter Problems}
40684067\end {eqnarray* }
40694068
40704069
4071- \end {enumerate }
4070+ \end {enumerate }
Original file line number Diff line number Diff line change @@ -1779,7 +1779,7 @@ \subsection{The matrix exponential and differential equations}
17791779cases. Consider the matrix $ A=\left [\matrix {1&1\cr 0&1}\right ]$ . This
17801780matrix does not have a basis of eigenvectors. So it cannot be
17811781diagonalized. However, in a homework problem, you showed that $ e^{tA}
1782- = \left [\matrix {e^t&te ^t\cr 0& e^t}\right ]$ . Thus the solution to
1782+ = \left [\matrix {e^t & t e ^t\cr 0 & e^t}\right ]$ . Thus the solution to
17831783\[
17841784\yy '(t) = \left [\matrix {1&1\cr 0&1}\right ]\yy (t)
17851785\]
@@ -1790,8 +1790,8 @@ \subsection{The matrix exponential and differential equations}
17901790is
17911791\[
17921792\yy (t) = e^{tA}\left [\matrix {2\cr 1\cr }\right ]
1793- =\left [\matrix {e^t&te ^t\cr 0& e^t}\right ]\left [\matrix {2\cr 1\cr }\right ]
1794- =\left [\matrix {2e^t+te ^t\cr e^t\cr }\right ]
1793+ =\left [\matrix {e^t & t e ^t\cr 0 & e^t}\right ]\left [\matrix {2\cr 1\cr }\right ]
1794+ =\left [\matrix {2e^t + t e ^t\cr e^t\cr }\right ]
17951795\]
17961796Notice that this solution involves a power of $ t$ in addition to
17971797exponentials.
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