Read the following set of vectors:

• v₁ = [1, 2, 3]

• v₂ = [2, 4, 6]

• v₃ = [3, 6, 9]

1. Determine whether the set {v₁, v₂, v₃} is linearly independent or dependent.

2. Justify your answer using the definition of linear dependence.

3. Reorganize the vectors and write any vector as a linear combination of the others (if applicable).

Extend this logic: Can a set of 4 vectors in R³ ever be linearly independent? Why or why not?