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Unformatted text preview: augmented matrix = 6 − 3 = 3. a redundant equation is eliminated to become 0 = 0 4 Proof (a) ⇔ (b): (b) means ∃ v = [ v 1 v 2 " v n ] T such that A v = [ a 1 a 2 " a n ] v = v 1 a 1 + v 2 a 2 + " + v n a n = b thus v is a solution, and A x = b is consistent. 5 * (a) ⇔ (c): Explained in Section 1.3. (a) ⇔ (d): Let [ R c ] be the reduced row echelon form of [ A b ], then from the definition of the reduced echelon form, R is the reduced row echelon form of A . (d) means that no nonzero entries of c appear at zero rows of R , which is exactly what (c) means....
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 Spring '09
 Fong

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