Les formules suivantes définissent-elles bien un changement de repère ? Dans ce cas, donner le changement de repère inverse.
\(\left\{ \begin{array}{l} x' = y - z + 1 \\ y' = -x - 4y + 5z + 2 \\ z' = x - 5y + 5z + 1 \end{array} \right.\)
\(\left\{ \begin{array}{l} x' = 5x + 4y + 3z - 2 \\ y' = 2x + 3y + z + 2 \\ z' = 4x - y + 3z + 2 \end{array} \right.\)
\(\left\{ \begin{array}{l} x' = -2x - 4y + 2z - 2 \\ y' = x + y - 5z + 1 \\ z' = -3x - 4y + 4z - 2 \end{array} \right.\)
\(\left\{ \begin{array}{l} x' = 3x - 5y + z + 2 \\ y' = 2x - y + z - 1 \\ z' = -3x - 4y - z - 5 \end{array} \right.\)
\(\left\{ \begin{array}{l} x' = 2x - z + 1 \\ y' = -2x + 2y + 2z - 2 \\ z' = -2x + y - z \end{array} \right.\)
\(\left\{ \begin{array}{l} x' = x - 2y - 3z + 5 \\ y' = -3x + 4y + z - 2 \\ z' = 2x - y + 6z + 3 \end{array} \right.\)