Fizaa A.

asked • 08/07/20

Please clerify this question!

Given the following 1st order linear homogeneous system:

LaTeX: \left\{\begin{array}{l}x^{\prime}(t) = - x(t) + 2 \, y(t)\\
\\
y^{\prime}(t) = - 2 \, x(t) + 3 \, y(t)
\end{array}\right. 

its coefficient matrix LaTeX: A = \left[\begin{array}{rr}
-1&2\\
-2&3
\end{array}\right]   has two repeated real eigenvalues LaTeX: \lambda_1 = \lambda_2 = 1     but only one independent eigenvector LaTeX: {\vec v} = \left[\begin{array}{r}
2\\
2
\end{array}\right]   

I got an answer below but I am not sure if it's right. Please Help!!LaTeX: C_1 \, e^{t} \, \left[\begin{array}{r}
2\\
2
\end{array}\right]
\, + \, C_2 \, e^t \, \left(\left[\begin{array}{r}
-1\\
1
\end{array}\right]
\, + \, t \, \left[\begin{array}{r}
2\\
2
\end{array}\right]


\right)

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