Let a subset W be the set of all vectors in R4 such that X₁ X2 X3 X4 = 0. Apply the theorem for conditions for a subspace to determine whether or not W is a subspace of R4. According to the theorem of conditions for a subspace, the nonempty subset W of the vector space V is a subspace of V if and only if it satisfies the following two conditions: (i) If u and v are vectors in W, then u + v is also in W. (ii) If u is in W and c is a scalar, then the vector cu is also in W. Select the correct choice below. .... OA. W is not a subspace of R4 because condition (ii) fails while condition (i) is satisfied. B. W is a subspace of R4 because it satisfies both of the conditions. OC. W is not a subspace of R4 because both conditions (i) and (ii) fail. OD. W is not a subspace of R4 because condition (i) fails while condition (ii) is satisfied. 4

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