$T(x)=T\left(\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right)=(2{x}_{1}+{x}_{3})\left(\begin{array}{c}1\\ 2\end{array}\right)+({x}_{2}-3{x}_{3})\left(\begin{array}{c}-1\\ 1\end{array}\right)$

1a) determine the matrix of the above transformation

1b) determine the reduced row echelon form of the matrix found in 1a

1c) based on your answer to part 1b, is the transformation T onto?

1d) based on your answer to part 1b, is the transformation T one-to-one?

1e) based on your answer to part 1b, determine the set of vectors $x$ in ${\mathbb{R}}^{3}$ for which $T(x)=0$. Write your answer in parametric vector form