Chapter 1.7, Problem 43E

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.)

43. (T/F-C) If ${\text{v}}_1,\dots ,{\text{v}}_4$ are in ${\text{R}}^4$ and $\left\{v_1,v_2,{\text{v}}_3\right\}$ is linearly dependent, then $\left\{v_1,v_2,{\text{v}}_3,{\text{v}}_4\right\}$ is also linearly dependent.