Answer
Yes, these vectors are linearly independent.
Work Step by Step
We multiply the first vector by $-\frac{1}{4}$ to get $(2,-3,1)$. Since this vector is equivalent to the second vector in the first two entries but not in the third entry, it cannot be that one is a constant multiple of the other. Hence, by the box at the top of page 59, the vectors are linearly independent.
