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(Solved): 3. If \( X \) is a solution of the IVP \[ X^{\prime}=\left[\begin{array}{cc} 1 & -2 \\ 2 & 1 \end{a ...




3. If \( X \) is a solution of the IVP
\[
X^{\prime}=\left[\begin{array}{cc}
1 & -2 \\
2 & 1
\end{array}\right] X, \quad X(0)
3. If \( X \) is a solution of the IVP \[ X^{\prime}=\left[\begin{array}{cc} 1 & -2 \\ 2 & 1 \end{array}\right] X, \quad X(0)=\left[\begin{array}{l} 0 \\ 4 \end{array}\right] \] then \( X\left(\frac{\pi}{4}\right)= \) (a) \( \left[\begin{array}{c}-4 \\ 0\end{array}\right] e^{\frac{\pi}{4}} \) (b) \( \left[\begin{array}{l}4 \\ 0\end{array}\right] e^{\frac{\pi}{4}} \) (c) \( \left[\begin{array}{l}0 \\ 4\end{array}\right] e^{\frac{\pi}{4}} \) (d) \( \left[\begin{array}{c}0 \\ -4\end{array}\right] e^{\frac{\pi}{4}} \) (e) \( \left[\begin{array}{l}4 \\ 4\end{array}\right] e^{\frac{\pi}{4}} \)


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