Unformatted text preview: augmented matrix [ a 1 a 2 a 3  b ] is consistent. Then, it is equivalent to say that b is a linear combination of a 1 , a 2 , a 3 . That is, b is in W . Now, as b is in W , b = c 1 a 1 + c 2 a 2 + c 3 a 3 for some scalars c 1 , c 2 , c 3 . Then a 1 + b = ( c 1 + 1) a 1 + c 2 a 2 + c 3 a 3 . Therefore, a 1 + b is also in W . 1...
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 Fall '06
 Sze
 Math, A1 A2 A3

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