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We are tasked with determining whether the sets of vectors provided in \( S \

Determine whether the following sets of vectors are linearly independent. Set A: S = {(2, -1, 3), (1, 1, -2), (3, -3, 8)}, Set B: T = {(1, 2, 1, 0, 0), (1, 1, 0, 1, 1), (1, 0, 0, 1, 1)}

Explore how to determine the linear independence of vector sets in both 3-dimensional and 5-dimensional spaces. This problem involves key linear algebra concepts such as vector spaces and the linear independence criterion. Suitable for university-level students studying linear algebra.

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