1.7.1 Linear transformations

Problem: Find out if the transformations are linear: \[ \begin{array}{l} A x=\left(3 x_{1}-2 x_{2}-x_{3}, 1, x_{1}+2 x_{2}+3\right), \\ B x=\left(3 x_{1}-2 x_{2}-x_{3}, 1, x_{1}^{3}+2 x_{2}+3 x_{3}\right), \\ C x=\left(3 x_{1}-2 x_{2}-x_{3}, x_{3}, x_{1}+2 x_{2}+3 x_{3}\right) . \end{array} \]