Unformatted text preview: 12 4 14 8 2 → 11 2 2 363 6 → 11 2 2 36 Thus x 3 is a free variable. The second row tells us that x 2 = 2 x 3 . The ±rst row tells us that x 1 = 2 + x 22 x 3 = 2. Thus we have x 1 = 2 x 2 = 2 x 3 x 3 free . 4. (a) all p ≥ 4 (b) all p ≤ 4 5. Since the number of columns of A T equals the number of rows of A , the product is de±ned. Since A T has p rows and A has p columns, A T A is p × p . Recalling that ( BC ) T = C T B T and ( B T ) T = B , we have ( A T A ) T = A T ( A T ) T = A T A....
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 Spring '03
 BUSS
 Math, Row echelon form, augmented matrix

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