Question

matrices: Which of the following transformations is linear? I'll post the matrices below

Answer 1

\[a) T(\left(\begin{matrix}x1 \\ x2\ \\ x3\end{matrix}\right) = \left(\begin{matrix}x3 \\ x2-x3\ \\ x1\end{matrix}\right)\]

Answer 2

\[b) T(\left(\begin{matrix}x1 \\ x2\ \\ x3\end{matrix}\right)) = \left(\begin{matrix}x1x3 \\ x2\ \\ (x1+x2)\end{matrix}\right)\]

Answer 3

\[c) T(\left(\begin{matrix}x1 \\ x2\ \\ x3\end{matrix}\right)) = \left(\begin{matrix}x3 \\ 1\end{matrix}\right)\]

Answer 4

\[d) T(\left(\begin{matrix}x1 \\ x2\ \\ x3 \end{matrix}\right)) = \left(\begin{matrix}x1 \\ x2\ \\ \left| x3 \right| \end{matrix}\right)\]

Answer 5

I know the answer is (a), but is it only because b) has x1x3, c) only has two rows, and d) has the absolute value?