Let W denote the subspace of R5 consisting of all the vectors having coordinates that sum to zero. The vectors
u 1 = (2, −3, 4, −5, 2), u2 = (−6, 9, −12, 15, −6),
u 3 = (3, −2, 7, −9, 1), u4 = (2, −8, 2, −2, 6),
u 5 = (−1, 1, 2, 1, −3), u6 = (0, −3, −18, 9, 12),
u 7 = (1, 0, −2, 3, −2), u8 = (2, −1, 1, −9, 7)
generate W. Find a subset of the set {u1, u2, . . . , u8} that is a basis for W.
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