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In the plane, consider a basis \((\Vect{u}, \Vect{v})\). Let \(\Vect{w}\) be a vector such that \(\Vect{w} = 3\Vect{u} - 2\Vect{v}\).
  1. What are the coordinates of \(\Vect{w}\) in the basis \((\Vect{u}, \Vect{v})\)?
  2. Let \(\Vect{z} = \Vect{u} + \Vect{w}\). Determine the coordinates of \(\Vect{z}\) in the basis \((\Vect{u}, \Vect{v})\).

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