Chapter 4, Problem 1CTA

For each statement that follows, answer true if the statement is always true and false otherwise. In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.
1. Let $L:{ℝ}^n\to {ℝ}^n$ be a linear transformation. If $L(x_1)=L(x_2)$ , then the vectors $x_1$ and $x_2$ must be equal.