Mathematics, 22.04.2020 01:10 chanahvanya
Consider the linear system yâ â²=Ayâ , where A is a real 2Ã2 constant matrix with repeated eigenvalues. Use the given information to determine the matrix A. Phase plane solution trajectories have horizontal tangents on the line y2=2y1 and vertical tangents on the line y1=0. The matrix A has a nonzero repeated eigenvalue and a21=â6.
Answers: 1
![A = \left[\begin{array}{ccc}1&0\\-2&1\end{array}\right]](/tpl/images/0616/7308/f740d.png)
![A = \left[\begin{array}{ccc}a_{11} &a_{12} \\a_{21} &a_{22} \end{array}\right]](/tpl/images/0616/7308/01003.png)
![\left[\begin{array}{ccc}y_{1}\\y_{2} \end{array}\right]' = \left[\begin{array}{ccc}a_{11} &a_{12} \\a_{21} &a_{22} \end{array}\right] + \left[\begin{array}{ccc}y_{1}\\y_{2} \end{array}\right]](/tpl/images/0616/7308/1e4f3.png)
...............(1)
................(2)
, 
, 
...........(2)
![A = \left[\begin{array}{ccc}3&0\\-6&3\end{array}\right]](/tpl/images/0616/7308/022e1.png)
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Consider the linear system yâ â²=Ayâ , where A is a real 2Ã2 constant matrix with repeated eigenvalu...
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