Part I If S1 and S2 are subspaces of a vector space V, then their union must also be a subspace of V. False True If S1 and S2 are subspaces of a vector space V, then their intersection must also be a subspace of V. False True Part II 1 1 4 2 1 Let A = 3 1 . The matrix v = d| is in the column space of 4 1 7 5 1 8 A if d = If vị is the first column of A and vz is the second column of A, then v = c1V1 + c2v2, where c¡ = and c2 = Part III 1 2 Let B 3 6 . The vector b is in the nullspace of A if 2 4 d

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