Chapter 1.7, Problem 39E

Each statement in Exercises 39—44 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21—28.)

39. (T/F-C) If $v_1,\mathrm{...},v_4$ are in $R^4$ and $v_3=2v_1+v_2$, then $\left\{v_1,v_2,v_3,v_4\right\}$ is linearly dependent.