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The set of all vectors in R 5 whose coordinates sum to zero forms a subspace....

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Advance Math

The set of all vectors in R 5 whose coordinates sum to zeroforms a subspace. The following vectors are a generating set forthe space. u1 = (2, −3, 4, −5, 2) u2 = (−6, 9, −12, 15, −6) u3 =(3, −2, 7, −9, 1) u4 = (2, −8, 2, −2, 6) u5 = (−1, 1, 2, 1 − 3) u6= (0, −3, −18, 9, 12) u7 = (1, 0, −2, 3, −2) u8 = (2, −1, 1, −9, 7)(a) Find a basis in the collection above. (b) Let L = {(1, 1, 1, 1,−4),(1, −1, 3, −2, −1)}. Find 6 vectors in the collection, say H,such that L ∪ H spans the entire space.

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