$$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle$$$
Your Input
Calculate $$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle$$$.
Solution
Multiply each coordinate of the vector by the scalar:
$$${\color{Brown}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left\langle 2 e^{2 t}, 0\right\rangle = \left\langle {\color{Brown}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left(2 e^{2 t}\right), {\color{Brown}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left(0\right)\right\rangle = \left\langle 1, 0\right\rangle$$$
Answer
$$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle = \left\langle 1, 0\right\rangle$$$A