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