Chapter 1.7, Problem 36E

Each statement in Exercises 33-38 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 I here than in Exercises 21 and 22.)

36. If v₁, . . . . , v₄ are in ℝ⁴ and v₃ is not a linear combination of v₁, v₂, v₄ then {v₁, v₂, v₃, v₄} is linearly independent.