Problem:
Find the coordinates of the vector \( X \) in the basis \( e^{\prime}=\left\{e_{1}^{\prime} ; e_{2}^{\prime} ; e_{3}^{\prime}\right\} \), if \( X=(1 ;-4 ; 8) \) in the basis \( e=\left\{e_{1} ; e_{2} ; e_{3}\right\} \) and
\[
\left\{\begin{array}{l}
e_{1}^{\prime}=e_{1}+e_{2}-3 e_{3} \\
e_{2}^{\prime}=\frac{3}{4} e_{1}-e_{2} \\
e_{3}^{\prime}=-e_{1}+e_{2}+e_{3}
\end{array}\right.
\]