Let T: V--->W be a linear transformation in which the zero vector in V is the only vector mapped to the zero vector in W by T. Prove that T is injective.
Let T: V--->W be a linear transformation in which the zero vector in V is the only vector mapped to the zero vector in W by T. Prove that T is injective.
Say that $\displaystyle T(\bold{x}) = T(\bold{y}) \implies T(\bold{x} - \bold{y}) = \bold{0}$ because it is a linear transformation. This means, $\displaystyle \bold{x}-\bold{y} = \bold{0}\implies \bold{x} = \bold{y}$.