1.1.5 Vector Algebra

Problem: Vector

X = (7; 7; 2)

is given in the basis

e = {e_{1}, e_{2}, e_{3}}

. Find the coordinates of

X

in the basis of

e^{'} = {e_{1}^{'}, e_{2}^{'}, e_{3}^{'}}

, where

{\begin{cases} e_{1}^{'} = e_{1} + e_{2} + \frac{6}{7} e_{3} \\ e_{2}^{'} = - 6 e_{1} - e_{2} \\ e_{3}^{'} = - e_{1} + e_{2} + e_{3} \end{cases}