Chapter 2.3, Problem 25EQ

Use the method of Example 2.23 and Theorem 2.6 to determine if the sets of vectors in Exercises 22-31 are linearly independent. If, for any of these, the answer can be determined by inspection (i.e., without calculation), state why. For any sets that are linearly dependent, find a dependence relationship among the vectors.

$\left[\begin{array}{l}0\\ 1\\ 2\end{array}\right],\left[\begin{array}{l}2\\ 1\\ 3\end{array}\right],\left[\begin{array}{l}2\\ 0\\ 1\end{array}\right]$