6. (5%) Let b1 = (1,0, -1,0,0), b2= (1,1,1,1,1),b3= (1,0,1,2,1) in R5 and w =span{b1,b2,b3}. Suppose c=(0,-6,-2,0,-2). Then what is the minimum value of ||c - u||for all possible choices of ? (A)(B) (C) (D) 2 (E) 3

4. (5%) Let A be an m by n matrix. Which statement is TRUE? (A) The null space of A is a subspace of the column space of AT (B) The dimension of the null space of A plus the dimension of the row space of A is (C) The null space of AT equals column space of A (D) The column space of A is orthogonal to the row space of AT (E) The direct sum of the row space of A and the null space of AT is Rm

6. (5%) Let b₁ = (1,0, -1,0,0), b₂= (1,1,1,1,1),b₃= (1,0,1,2,1) in R⁵ and w =span{b₁,b₂,b₃}. Suppose c=(0,-6,-2,0,-2). Then what is the minimum value of ||c - u||for all possible choices of ?
(A)
(B)
(C)
(D) 2
(E) 3

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