In Problems 15–18, apply Theorem 4 (that is, calculate a determinant) to determine whether the given vectors u, v, and w are linearly dependent or independent.

u = (5, -2, 4), v = (2, -3, 5), w = (4, 5, -7)

THEOREM 4 Three Linearly Independent Vectors The vectors u = (, U2, U3), V = (v, V2, V3), and w = (w, W2, W3) are linearly independent if and only if U V W U2 V2 W2 0. U3 V3 W3 (8)