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Decide whether the transformation L :R->R defined by L(x_{1}, x_{2}, x_{3}) = (3x_{2} + x_{3}, 4x_{1} + x_{2}, x_{1} - 5) is linear or not.

Decide whether the transformation L :R->R defined by L(x_{1}, x_{2}, x_{3}) = (3x_{2} + x_{3}, 4x_{1} + x_{2}, x_{1} - 5) is linear or not. Justify your answer mathematically!

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