Find the volume \( V(S) \) of the parallelepiped \( S \) in \( \mathbf{R}^3 \) determined by the vectors:
(a) \( u_1 = (1,1,1) \), \( u_2 = (1, 3, -4) \), \( u_3 = (1, 2, -5) \).
(b) \( u_1 = (1,2,4) \), \( u_2 = (2, 1, -3) \), \( u_3 = (5,7,9) \).
linear-algebradeterminantsvolumeparallelepipedscalar-triple-productlinear-dependencecoplanar-vectorssarrus-rulematrix-determinant3x3-matrixabsolute-valuegeometric-interpretation
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