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$\begin{cases} \dfrac{dx_1}{dt}=x_2\\[2mm] \dfrac{dx_2}{dt} =-\dfrac{x_2+5x_1}{2} \end{cases}$

$\mbox{None of the above}$

$\begin{cases} \dfrac{dx_1}{dt}=x_2\\[2mm] \dfrac{dx_2}{dt} =-\dfrac{x_2+2x_1}{5} \end{cases}$

$\begin{cases} \dfrac{dx_1}{dt}=-\dfrac{x_2+5x_1}{2}\\[2mm] \dfrac{dx_2}{dt} =x_2 \end{cases}$

$\begin{cases} \dfrac{dx_1}{dt}=-\dfrac{x_2+2x_1}{5}\\[2mm] \dfrac{dx_2}{dt} =x_2 \end{cases}$

	$H_1 \ \mbox{is a vector space and} \ H_2 \ \mbox{is a vector space.}$
	$H_1 \ \mbox{is a vector space, but} \ H_2 \ \mbox{is not a vector space.}$
	$H_1 \ \mbox{is not a vector space and} \ H_2 \ \mbox{is not a vector space.}$
	$H_1 \ \mbox{is not a vector space, but} \ H_2 \ \mbox{is a vector space.}$

	$\mbox{None of the above}$
	$\mbox{If} \ \lambda \ \mbox{has multiplicity 1, then the corresponding eigenspace has dimension 1.}$
	$\mbox{All of the above}$
	$\mbox{If} \ \lambda \ \mbox{has multiplicity 3, then the corresponding eigenspace has dimension 3.}$
	$\mbox{If} \ \lambda \ \mbox{has multiplicity 2, then the corresponding eigenspace has dimension 2.}$

	$\mbox{linearly dependent and do not span} \ \mathbb{P}_2.$
	$\mbox{linearly independent and span} \ \mathbb{P}_2.$
	$\mbox{linearly independent and do not span} \ \mathbb{P}_2.$
	$\mbox{linearly dependent and span} \ \mathbb{P}_2.$

	$\dfrac{1}{e}\left [ \begin{array}{r} 1\\[3mm] 0\\[3mm] 0 \end{array} \begin{array}{r} -\pi\\[3mm] -e\\[3mm] 0 \end{array} \begin{array}{c} \sqrt{2}\\[3mm] 0\\[3mm] e \end{array} \right ]$
	$\dfrac{1}{e}\left [ \begin{array}{r} -1\\[3mm] 0\\[3mm] 0 \end{array} \begin{array}{r} -\pi\\[3mm] -e\\[3mm] 0 \end{array} \begin{array}{c} -\sqrt{2}\\[3mm] 0\\[3mm] -e \end{array} \right ]$
	$\dfrac{1}{e} \left [ \begin{array}{r} 1\\[3mm] 0\\[3mm] 0\end{array} \begin{array}{r} \pi\\[3mm] e\\[3mm] 0\end{array} \begin{array}{c} -\sqrt{2}\\[3mm] 0\\[3mm] -e \end{array} \right ]$
	$\mbox{None of the above}$
	$\dfrac{1}{e}\left [ \begin{array}{r} 1\\[3mm] 0\\[3mm] 0 \end{array} \begin{array}{r} -\pi\\[3mm] e\\[3mm] 0 \end{array} \begin{array}{c} -\sqrt{2}\\[3mm] 0\\[3mm] e \end{array} \right ]$

Test!

	$\left [ \begin{array}{c} 0\\[1mm] 1\\[1mm] 0\\[1mm] 0 \end{array} \right ]+ x_2\left [ \begin{array}{r} 0\\[1mm] 0\\[1mm] 1\\[1mm] -1 \end{array} \right ]$
	$\mbox{None of the above}$
	$\left [ \begin{array}{c} 1\\[1mm] 0\\[1mm] 0\\[1mm] 0 \end{array} \right ]+ x_1\left [ \begin{array}{r} 0\\[1mm] 0\\[1mm] -1\\[1mm] 1 \end{array} \right ]$
	$\left [ \begin{array}{c} 0\\[1mm] 0\\[1mm] 1\\[1mm] 1 \end{array} \right ]+ x_3\left [ \begin{array}{r} 0\\[1mm] 0\\[1mm] 0\\[1mm] 1 \end{array} \right ]$
	$\left [ \begin{array}{c} 0\\[1mm] 0\\[1mm] 1\\[1mm] 0 \end{array} \right ]+ x_4\left [ \begin{array}{r} 0\\[1mm] 0\\[1mm] -1\\[1mm] -1 \end{array} \right ]$

	$\mbox{None of the above}$
	$\left [ \begin{array}{rr} \sin \phi \\ \cos \phi \end{array} \begin{array}{r} -\cos \phi\\ \sin \phi \end{array} \right ]$
	$\left [ \begin{array}{r} \sin \phi\\ \cos \phi\end{array} \begin{array}{r} -\sin \phi\\ \cos \phi \end{array} \right ]$
	$\left [ \begin{array}{r} \cos \phi\\ \sin \phi\end{array} \begin{array}{r} -\cos \phi\\ \sin \phi \end{array} \right ]$
	$\left [ \begin{array}{r} \cos \phi \\ \sin \phi\end{array} \begin{array}{r} -\sin \phi\\ \cos \phi \end{array} \right ]$

	${\bf x}(t) =e^{-2t}\left (c_1 \left [ \begin{array}{r} \cos 2t\\[2mm] -\sin 2t \end{array} \right ]+ c_2 \left [ \begin{array}{r} \sin 2t\\[2mm] \cos 2t \end{array} \right ] \right )$
	${\bf x}(t)=e^{-t}\left (c_1 \left [ \begin{array}{r} \cos 2t\\[2mm] -\sin 2t \end{array} \right ]+ c_2 \left [ \begin{array}{r} \sin 2t\\[2mm] \cos 2t \end{array} \right ] \right )$
	$\mbox{None of the above}$
	${\bf x}(t)=e^{-2t}\left (c_1 \left [ \begin{array}{r} \cos 2t\\[2mm] \sin 2t \end{array} \right ]+ c_2 \left [ \begin{array}{r} \sin 2t\\[2mm] \cos 2t \end{array} \right ] \right )$
	${\bf x}(t)=e^{-t}\left (c_1 \left [ \begin{array}{r} \cos 2t\\[2mm] \sin 2t \end{array} \right ]+ c_2 \left [ \begin{array}{r} \sin 2t\\[2mm] \cos 2t \end{array} \right ] \right )$

	${\bf x}(t)=e^{3t}\left (c_1 \left [ \begin{array}{c} 1\\[2mm] 3 \end{array} \right ]+ c_2 \left [ \begin{array}{c} t\\[2mm] 1+3t \end{array} \right ] \right )$
	${\bf x}(t)=e^{3t}\left (c_1 \left [ \begin{array}{c} 3\\[2mm] 1 \end{array} \right ]+ c_2 \left [ \begin{array}{c} t\\[2mm] 1+3t \end{array} \right ] \right )$
	${\bf x}(t)= e^{3t}\left (c_1 \left [ \begin{array}{c} 1\\[2mm] 3 \end{array} \right ]+ c_2 \left [ \begin{array}{c} 1+3t\\[2mm] t \end{array} \right ] \right )$
	$\mbox{None of the above}$
	${\bf x}(t)=e^{3t}\left (c_1 \left [ \begin{array}{c} 3\\[2mm] 1 \end{array} \right ]+ c_2 \left [ \begin{array}{c} 1+3t\\[2mm] t \end{array} \right ] \right )$