(Solved): Problem 1 ( 4 pts) Consider the linear transformation L:R3R2 given by Lx1x2 ...

Problem 1 ( 4 pts) Consider the linear transformation $L:{\mathbb{R}}^3?{\mathbb{R}}^2$ given by $L??\begin{array}{l}{x}_1\\ x_2\\ x_3\end{array}??=\left[\begin{array}{c}0\\ x_2?x_3\end{array}\right]$ (a) $(0.5\mathrm{pts})$ is $L$ a linear operator? YES/NO (b) (1 pt) Find a basis for Range $(L)=L\left({\mathbb{R}}^3\right)$. (c) (1 pt) Find a basis for the kernel of $L,\ker (L)$. (d) (0.5 pts) is L onto? YES/NO (e) $(0.5\mathrm{pts})$ is $L$ one-to-one? YES/NO (f) $(0.5\mathrm{pts})$ Consider ordered bases $E=??\begin{array}{l}1\\ 1\\ 5\end{array}?,?\begin{array}{l}1\\ 3\\ 2\end{array}?,?\begin{array}{l}0\\ 0\\ 1\end{array}??$ and $F=\left\{\left[\begin{array}{l}1\\ 0\end{array}\right]?\left[\begin{array}{l}2\\ 1\end{array}\right]\right\}$ for ${\mathbb{R}}^3$ and ${\mathbb{R}}^2$, respectively. Consider further that the reduced row echelon form of Determine the matrix $A$ representing $L$ with respect to bases $E$ and $F$.