A.10.7: Section 10.7 Answers
- Page ID
- 43740
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. \(\left[\begin{array}{c}{5e^{4t}+e^{-3t}(2+8t)}\\[4pt]{-e^{4t}-e^{-3t}(1-4t)}\end{array}\right]\)
2. \(\left[\begin{array}{c}{13e^{3t}+3e^{-3t}}\\[4pt]{-e^{3t}-11e^{-3t}}\end{array}\right]\)
3. \(\frac{1}{9}\left[\begin{array}{c}{7-6t}\\[4pt]{-11+3t}\end{array}\right]\)
4. \(\left[\begin{array}{c}{5-3e^{t}}\\[4pt]{-6+5e^{t}}\end{array}\right]\)
5. \(\left[\begin{array}{c}{e^{-5t}(3+6t)+e^{-3t}(3-2t)}\\[4pt]{-e^{-5t}(3+2t)-e^{-3t}(1-2t)}\end{array}\right]\)
6. \(\left[\begin{array}{c}{t}\\[4pt]{0}\end{array}\right]\)
7. \(-\frac{1}{6}\left[\begin{array}{c}{2-6t}\\[4pt]{7+6t}\\[4pt]{1-12t}\end{array}\right]\)
8. \(-\frac{1}{6}\left[\begin{array}{c}{3e^{t}+4}\\[4pt]{6e^{t}-4}\\[4pt]{10}\end{array}\right]\)
9. \(\frac{1}{18}\left[\begin{array}{c}{e^{t}(1+12t)-e^{-5t}(1+6t)}\\[4pt]{-2e^{t}(1-6t)-e^{-5t}(1-12t)}\\[4pt]{e^{t}(1+12t)-e^{-5t}(1+6t)}\end{array}\right]\)
10. \(\frac{1}{3}\left[\begin{array}{c}{2e^{t}}\\[4pt]{e^{t}}\\[4pt]{2e^{t}}\end{array}\right]\)
11. \(\left[\begin{array}{c}{t\sin t}\\[4pt]{0}\end{array}\right]\)
12. \(-\left[\begin{array}{c}{t^{2}}\\[4pt]{2t}\end{array}\right]\)
13. \((t-1)(\ln |t-1|+t)\left[\begin{array}{c}{1}\\[4pt]{-1}\end{array}\right]\)
14. \(\frac{1}{9}\left[\begin{array}{c}{5e^{2t}-e^{-3t}}\\[4pt]{e^{3t}-5e^{-2t}}\end{array}\right]\)
15. \(\frac{1}{4t}\left[\begin{array}{c}{2t^{3}\ln |t|+t^{3}(t+2)}\\[4pt]{2\ln |t|+3t-2}\end{array}\right]\)
16. \(\frac{1}{2}\left[\begin{array}{c}{te^{-t}(t+2)+(t^{3}-2)}\\[4pt]{te^{t}(t-2)+(t^{3}+2)}\end{array}\right]\)
17. \(-\left[\begin{array}{c}{t}\\[4pt]{t}\\[4pt]{t}\end{array}\right]\)
18. \(\frac{1}{4}\left[\begin{array}{c}{-3e^{t}}\\[4pt]{1}\\[4pt]{e^{-t}}\end{array}\right]\)
19. \(\left[\begin{array}{c}{2t^{2}+t}\\[4pt]{t}\\[4pt]{-t}\end{array}\right]\)
20. \(\frac{e^{t}}{4t}\left[\begin{array}{c}{2t+1}\\[4pt]{2t-1}\\[4pt]{2t+1}\end{array}\right]\)
22.
- \({\bf y'}=\left[\begin{array}{cccc}{0}&{1}&{\ldots }&{0}\\[4pt]{0}&{0}&{\ldots }&{0}\\[4pt]{\vdots }&{\vdots }&{\ddots }&{\vdots }\\[4pt]{0}&{0}&{\ldots }&{1}\\[4pt]{-P_{n}(t)/P_{0}(t)}&{-P_{n-1}/P_{0}(t)}&{\ldots }&{-P_{1}(t)/P_{0}(t)}\end{array}\right]{\bf y}+\left[\begin{array}{c}{0}\\[4pt]{0}\\[4pt]{\vdots }\\[4pt]{F(t)/P_{0}(t)}\end{array}\right]\)
- \(\left[\begin{array}{cccc}{y_{1}}&{y_{2}}&{\ldots }&{y_{n}}\\[4pt]{y'_{1}}&{y'_{2}}&{\ldots }&{y'_{n}}\\[4pt]{\vdots }&{\vdots }&{\ddots }&{\vdots }\\[4pt]{y_{1}^{(n-1)}}&{y_{2}^{(n-1)}}&{\ldots }&{y_{n}^{(n-1)}}\end{array}\right]\)