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$\hspace{-6mm}{\bf v}_1(t), {\bf v}_2(t), {\bf v}_3(t) \ \mbox{are linearly independent,}\\ \mbox{since} \ {\bf v}_1(t_0), {\bf v}_2(t_0), {\bf v}_3(t_0) \ \mbox{are linearly independent for any real number} \ t_0$

$\hspace{-6mm}{\bf v}_1(t), {\bf v}_2(t), {\bf v}_3(t) \ \mbox{are linearly dependent,}\\ \mbox{since} \ {\bf v}_1(t_0), {\bf v}_2(t_0), {\bf v}_3(t_0) \ \mbox{are linearly dependent for any real number} \ t_0$

$\hspace{-6mm}{\bf v}_1(t), {\bf v}_2(t), {\bf v}_3(t) \ \mbox{are linearly independent,} \\ \mbox{since} \ {\bf v}_1(t_0), {\bf v}_2(t_0), {\bf v}_3(t_0) \ \mbox{are linearly independent if} \ t_0=1$

$\mbox{None of the above}$

$\hspace{-6mm}{\bf v}_1(t), {\bf v}_2(t), {\bf v}_3(t) \ \mbox{are linearly dependent,}\\ \mbox{since} \ {\bf v}_1(t_0)+{\bf v}_2(t_0)={\bf v}_3(t_0) \ \mbox{if} \ t_0=0$

Test:	DELA - 2018 Fall - Midterm II
Number of Questions:	6
Time:

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

	$\left [ \begin{array}{c}4 \\ 16 \end{array} \begin{array}{c}9 \\ 25 \end{array} \right ]$
	$\left [ \begin{array}{r} 2\\ 3 \end{array} \begin{array}{r} 4\\ 5 \end{array}\right ]$
	$\left [ \begin{array}{r}5\\ -4 \end{array} \begin{array}{r}-3\\ 2 \end{array} \right ]$
	$\left [ \begin{array}{r} 25 \\ -16 \end{array} \begin{array}{r} -9\\ 4 \end{array} \right ]$
	$\mbox{None of the above}$

	$\mbox{None of the above}$
	$S({\bf x})=B{\bf x}, \ \mbox{where} \ B=\left [ \begin{array}{r} 12\\ 0\\ -6 \end{array} \begin{array}{r} 0\\ 4\\ 0 \end{array} \begin{array}{r} 0\\ 0\\ 3 \end{array} \right ]$
	$S({\bf x})=B{\bf x}, \ \mbox{where} \ B=\left [ \begin{array}{c} 1\\ 0\\ -1/2 \end{array} \begin{array}{c} 0\\ 1/3\\ 0\end{array} \begin{array}{c}0\\0\\1/4 \end{array} \right ]$
	$S({\bf x})=B{\bf x}, \ \mbox{where} \ B=\left [ \begin{array}{r} 12\\ 0\\ 0 \end{array} \begin{array}{r} 0\\ 4\\ 0 \end{array} \begin{array}{r} -6\\ 0\\ 3 \end{array} \right ]$
	$S({\bf x})=B{\bf x}, \ \mbox{where} \ B=\left [ \begin{array}{c} 1\\ 0\\ 0 \end{array} \begin{array}{c} 0\\ 1/3\\ 0 \end{array} \begin{array}{c} -1/2\\ 0\\ 1/4 \end{array} \right ]$

	$\mbox{None of the above}$
	$\mbox{span} \{(1, 0, 2)\}$
	$\mbox{span} \{(1, 2, 0), (0, 0, 1)\}$
	$\mbox{span} \{(1, 0, 1)\}$
	$\mbox{span} \{(1, 1, 0), (0, 0, 1)\}$

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	${\bf x}(t)= c_1e^{-t}\left [ \begin{array}{r} 1\\[2mm] 2 \end{array} \right ]+c_2e^{-t}\left [ \begin{array}{c} 1-2t\\[2mm] 2t \end{array} \right ]$
	${\bf x}(t)= c_1e^{-t}\left [ \begin{array}{r} -2\\[2mm] 2 \end{array} \right ]+c_2e^{-t}\left [ \begin{array}{c} 1-2t\\[2mm] 2t \end{array} \right ]$
	${\bf x}(t)= c_1e^{-t}\left [ \begin{array}{r} 1\\[2mm] 2 \end{array} \right ]+c_2e^{-t}\left [ \begin{array}{c} 1-t\\[2mm] 2t \end{array} \right ]$
	$\mbox{None of the above}$
	${\bf x}(t)= c_1e^{-t}\left [ \begin{array}{r} -2\\[2mm] 2 \end{array} \right ]+c_2e^{-t}\left [ \begin{array}{c} 1-t\\[2mm] 2t \end{array} \right ]$