Math Challenges

Submissions for Problem #76

Problem #76

a) Compute the eigenvalues,
b) Compute the associated eigenvectors,
c) Specify the straight-line solution for each eigenvector,
d) Express an equation for the general solution Y(t).

\[ \frac{d\mathbf{Y}}{dt}=\begin{pmatrix}-3 & -1\\ 0 & -1\end{pmatrix}\mathbf{Y} \]

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zapwai

Solution: \( \displaylines{\lambda_1=-3,\lambda_2=-1\\ v_1=\begin{pmatrix}1\\ 0\end{pmatrix},v_2=\begin{pmatrix}1\\ -2\end{pmatrix}\\ \mathbf{Y}=c_1e^{-3t}\begin{pmatrix}1\\ 0\end{pmatrix}+c_2e^{-t}\begin{pmatrix}1\\ -2\end{pmatrix}} \)