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Problem 1 ( 4 pts) Consider the linear transformation $L:R_{3}?R_{2}$ given by $L??????x_{1}x_{2}x_{3}???????=[0x_{2}?x_{3}?]$ (a) $(0.5pts)$ is $L$ a linear operator? YES/NO (b) (1 pt) Find a basis for Range $(L)=L(R_{3})$. (c) (1 pt) Find a basis for the kernel of $L,ker(L)$. (d) (0.5 pts) is L onto? YES/NO (e) $(0.5pts)$ is $L$ one-to-one? YES/NO (f) $(0.5pts)$ Consider ordered bases $E=???????115????,???132????,???001????????$ and $F={[10?]?[21?]}$ for $R_{3}$ and $R_{2}$, respectively. Consider further that the reduced row echelon form of Determine the matrix $A$ representing $L$ with respect to bases $E$ and $F$.

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