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[10] 7. Suppose W = { x 1 x 2 x 3 x 4 x 5 | x 1 = x 3 , x 1 + x 2 = x 5 , x 2 = x 5 - x 3 , x 4 = x 5 } . Find a basis for W and determine its dimension. 10 of 13

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8. Let A = 1 0 1 0 1 - 1 1 1 0 0 - 1 1 , and B = 0 0 0 1 . [3] (a) Find a basis of the column space of A . [3] (b) Prove that B does not belong to the column space of A . [4] (c) Find a least-squares solution X of the equation AX = B . 12 of 13

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