The Solution of the System $X ^ { \prime } = \left( \begin{array} { c c } - 3 & - 1 \\1 & - 1\end{array} \right) X$

The solution of the system $X ^ { \prime } = \left( \begin{array} { c c } - 3 & - 1 \\1 & - 1\end{array} \right) X$ is

A) $\mathbf { X } = c _ { 1 } \left( \begin{array} { c } - 1 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left[ \left( \begin{array} { c } - 1 \\1\end{array} \right) t e ^ { - 2 t } + \left( \begin{array} { l } 1 \\0\end{array} \right) e ^ { - 2 t } \right]$
B) $\mathbf { X } = c _ { 1 } \left( \begin{array} { c } - 1 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { c } - 1 \\1\end{array} \right) t e ^ { - 2 t } + c _ { 3 } \left( \begin{array} { l } 1 \\0\end{array} \right) e ^ { - 2 t }$
C) $X = c _ { 1 } \left( \begin{array} { c } - 1 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { c } 1 \\- 1\end{array} \right) t e ^ { - 2 t }$
D) $X = c _ { 1 } \left( \begin{array} { c } - 1 \\1\end{array} \right) e ^ { - 2 t } + c _ { 2 } \left( \begin{array} { l } 1 \\2\end{array} \right) e ^ { - t }$
E) none of the above

Correct Answer:

Verified

Unlock this answer now
Get Access to more Verified Answers free of charge

Access For Free