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Unformatted text preview: N ( A ) = nullity( A ) = nrank A = n1 . 16. (a) (Proof of Lemma 3.2.1) Suppose that each of X 1 ,...,X r is a linear combination of Y 1 ,...,Y s . Then X i = s X j =1 a ij Y j , (1 i r ) . Now let X = r i =1 x i X i be a linear combination of X 1 ,...,X r . Then X = x 1 ( a 11 Y 1 + + a 1 s Y s ) + + x r ( a r 1 Y 1 + + a rs Y s ) = y 1 Y 1 + + y s Y s , where y j = a 1 j x 1 + + a rj x r . Hence X is a linear combination of Y 1 ,...,Y s . Another way of stating Lemma 3.2.1 is h X 1 ,...,X r i h Y 1 ,...,Y s i , (1) 38...
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.
 Fall '10
 Dreibelbis

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