Final answer:
To determine whether a set of vectors is linearly independent or dependent, create a system of equations with the given vectors and solve for the coefficients. If there exists a non-trivial solution, the set is linearly dependent. In this case, the set S is linearly dependent.
Step-by-step explanation:
To determine whether a set of vectors is linearly independent or dependent, we can create a system of equations with the given vectors and solve for the coefficients. If there exists a non-trivial solution, then the set is linearly dependent. Otherwise, the set is linearly independent.
In this case, we have the set S = {(-2, 1, 3), (2, 8, -3), (2, 3, -3)}. We can represent each vector as a linear combination of the three variables x, y, and z. Setting up the system of equations, we get:
-2x + 2y + 2z = 0
x + 8y + 3z = 0
3x - 3y - 3z = 0
We can solve this system using Gaussian elimination or a calculator. After solving, we find that the system has a non-trivial solution. Therefore, the set S is linearly dependent.