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In 3D space, consider a basis \((\Vect{e_1}, \Vect{e_2}, \Vect{e_3})\). Let \(\Vect{x} = \Vect{e_1} + 4\Vect{e_3}\) and \(\Vect{y} = 2\Vect{e_2} - \Vect{e_3}\).
  1. Give the coordinates of \(\Vect{x}\) and \(\Vect{y}\) in the basis \((\Vect{e_1}, \Vect{e_2}, \Vect{e_3})\).
  2. Determine the coordinates of the vector \(\Vect{z} = \Vect{x} + 2\Vect{y}\) in the same basis.

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