Chapter 4.1, Problem 21E

A linear transformation $L:V\to W$ is said to be one−to−one if $L(v_1)=L(v_2)$ implies that $v_1=v_2$ (i.e., no two distinct vectors $v_1,v_2$ in V get mapped into the same vector $w\in W$ ). Show that L is one−to−one if and only if $\ker (L)=\left\{0_v\right\}$ .