Determine whether the vectors v1 = (1, 2) and v2 = (3, 6) are linearly independent.

Step 1: Recall the idea of linear independence.

Two vectors are linearly dependent if one can be written as a scalar multiple of the other.

Step 2: Compare the vectors.

v1 = (1, 2)
v2 = (3, 6)

Multiply v1 by 3:

3v1 = 3(1, 2)
3v1 = (3, 6)

Step 3: Compare with v2.

We have:
3v1 = v2

Therefore, one vector is a scalar multiple of the other.

Step 4: State the conclusion.

Because v2 can be written as 3v1, the vectors are linearly dependent.

Therefore, v1 and v2 are not linearly independent.