The Wronskian of the vector functions $X _ { 1 } = \left( \begin{array} { c }
1 \
- 1
\end{array} \right) e ^ { - 2 t }$ and $X _ { 2 } = \left( \begin{array} { l }
3 \
5
\end{array} \right) e ^ { 6 t }$ is
A) $8 e ^ { 4 t }$
B) $2 e ^ { 4 t }$
C) $- 8 e ^ { 4 t }$
D) $- 2 e ^ { 4 t }$
E) $15 e ^ { 4 t }$

Question

The Wronskian of the vector functions $X _ { 1 } = \left( \begin{array} { c } 
1 \
- 1
\end{array} \right) e ^ { - 2 t }$ and $X _ { 2 } = \left( \begin{array} { l } 
3 \
5
\end{array} \right) e ^ { 6 t }$ is
A) $8 e ^ { 4 t }$
B) $2 e ^ { 4 t }$
C) $- 8 e ^ { 4 t }$
D) $- 2 e ^ { 4 t }$
E) $15 e ^ { 4 t }$

Quizplus · Accepted Answer

The Wronskian of the vector functions $X _ { 1 } = \left( \begin{array} { c } 1 \- 1\end{array} \right) e ^ { - 2 t }$ and $X _ { 2 } = \left( \begin{array} { l } 3 \5\end{array} \right) e ^ { 6 t }$ is$$W(X_1,X_2)=\begin{vmatrix} 1e^{-2t} & 3e^{6t} \\ -1e^{-2t} & 5e^{6t} \end{vmatrix}$$$$=1\times5e^{6t}-(-1)\times3e^{6t}$$$$=5e^{6t}+3e^{6t}=8e^{6t}$$

The Wronskian of the Vector Functions X1=(1−1)e−2tX _ { 1 } = \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - 2 t }X1​=(1−1​)e−2t

The Wronskian of the Vector Functions $X _ { 1 } = \left( \begin{array} { c } 1 \\- 1\end{array} \right) e ^ { - 2 t }$