(a) Determine which of the following maps are linear (giving reasons for your answers). f: R_{3}-\rightarrow R_{2} \quad\left[x_{1, X 2, X 3}\right\} 7-\rightarrow[x 2+1, x 3-1\} f: \mathrm{R} 3-\rightarrow \mathrm{R}

\quad[x 1, X 2, X 3\} 7-\rightarrow X 1 \times 2 \times 3 f: \mathrm{R} 3-\rightarrow \mathrm{R} 3 \quad[X 1, X 2, X 3\} 7-\rightarrow[X 1+X 2+2 X 3,0, X 2\}