Chapter 6.2, Problem 7P

Consider the vectors

${\text{x}}_{\text{1}}\left(t\right)=\left(\begin{array}{c}{e}^t\\ 2e^t\\ -e^t\end{array}\right)$, ${\text{x}}_{\text{2}}\left(t\right)=\left(\begin{array}{c}{e}^{-t}\\ -2e^{-t}\\ e^{-t}\end{array}\right)$, ${\text{x}}_{\text{3}}\left(t\right)=\left(\begin{array}{c}2e^{4t}\\ 2e^{4t}\\ -8e^{4t}\end{array}\right)$

and let $\text{X}\left(t\right)$ be the matrix whose column are the vectors ${\text{x}}_1\left(t\right),{\text{x}}_2\left(t\right),{\text{x}}_3\left(t\right)$. Compare the amounts of work between the following two methods for obtaining

$\text{W}\left[{\text{x}}_{\text{1}}{\text{,x}}_{\text{2}}{\text{,x}}_{\text{3}}\right]\left(0\right)$:

Method $1$: First find $\left|\text{X}\left(t\right)\right|$ and then set $t=0$.

Method $2$: Evaluate $\text{X}\left(t\right)$ at $t=0$ and then find $\left|\text{X}\left(0\right)\right|$.