37: Section 10.1 Answers

1. \(\bf{y'}=\left[\begin{array}{cc}{2}&{4}\\{4}&{2}\end{array}\right]{\bf y}\)

2. \(\bf{y'}=\left[\begin{array}{cc}{-2}&{-2}\\{-5}&{1}\end{array}\right]{\bf y}\)

3. \(\bf{y'}=\left[\begin{array}{cc}{-4}&{-10}\\{3}&{7}\end{array}\right]{\bf y}\)

4. \(\bf{y'}=\left[\begin{array}{cc}{2}&{1}\\{1}&{2}\end{array}\right]{\bf y}\)

5. \(\bf{y'}=\left[\begin{array}{ccc}{-1}&{2}&{3}\\{0}&{1}&{6}\\{0}&{0}&{-2}\end{array}\right]{\bf y}\)

6. \(\bf{y'}=\left[\begin{array}{ccc}{0}&{2}&{2}\\{2}&{0}&{2}\\{2}&{2}&{0}\end{array}\right]{\bf y}\)

7. \(\bf{y'}=\left[\begin{array}{ccc}{-1}&{2}&{2}\\{2}&{-1}&{2}\\{2}&{2}&{-1}\end{array}\right]{\bf y}\)

8.\(\bf{y'}=\left[\begin{array}{ccc}{3}&{-1}&{-1}\\{-2}&{3}&{2}\\{4}&{-1}&{-2}\end{array}\right]{\bf y}\)

9. \(\bf{y'}=\left[\begin{array}{cc}{1}&{1}\\{-2}&{4}\end{array}\right]{\bf y},\quad {\bf y}(0)=\left[\begin{array}{c}{1}\\{0}\end{array}\right]\)

10. \(\bf{y'}=\left[\begin{array}{cc}{5}&{3}\\{-1}&{1}\end{array}\right]{\bf y},\quad {\bf y}(0)=\left[\begin{array}{c}{9}\\{-5}\end{array}\right]\)

11. \(\bf{y'}=\left[\begin{array}{ccc}{6}&{4}&{4}\\{-7}&{-2}&{-1}\\{7}&{4}&{3}\end{array}\right]{\bf y},\quad {\bf y}(0) =\left[\begin{array}{c}{3}\\{-6}\\{4}\end{array}\right]\)

12. \(\bf{y'}=\left[\begin{array}{ccc}{8}&{7}&{7}\\{-5}&{-6}&{-9}\\{5}&{7}&{10}\end{array}\right]{\bf y},\quad {\bf y}(0)=\left[\begin{array}{c}{2}\\{-4}\\{3}\end{array}\right]\)

13. \({\bf y'}=\left[\begin{array}{cc}{-3}&{2}\\{-5}&{3}\end{array}\right] + \left[\begin{array}{c}{3-2t}\\{6-3t}\end{array}\right]\)

14. \({\bf y'}=\left[\begin{array}{cc}{3}&{1}\\{-1}&{1}\end{array}\right]{\bf y} + \left[\begin{array}{c}{-5e^{t}}\\{e^{t}}\end{array}\right]\)

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