Each statement in Exercises 33–38 is either true (in

QUESTION:

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 here than in Exercises 21 and 22.)

If \(\mathbf{v}_{1}, \ldots, \mathbf{v}_{4}\) is a linearly independent set of vectors in \(\mathbb{R}^{4}\), then \(\left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\}\) is also linearly independent. [Hint: Think about \(x_{1} \mathbf{v}_{1}+x_{2} \mathbf{v}_{2}+x_{3} \mathbf{v}_{3}+0 \cdot \mathbf{v}_{4}=\mathbf{0}\).]