Unformatted text preview: B can be free modiﬁed without aﬀecting AB . (b) By the ﬁrst part of Theorem 13, or what is the same, V.I.F. 4 , ( AB ) 1 ,j = (row 1 of A ) · (column j of B ) . Since (row 1 of A ) 6 = 0, by changing (column j of B ), we can change the value of A 1 ,j . (The same sort of argument wold apply to A 2 ,j as well). Therefore, none of the columns of B can be freely modiﬁed. 5.13 Let C be a 2 by 2 matrix such that C h 1 2 i = h 2 1 i and C h 2 1 i = h1 1 i Using the given information, ﬁnd 2 × 2 matrices A and B so that CA = B , and then solve for C . SOLUTION By V.I.F. 3 , if A = [ v 1 , v 2 ], then CA = [ C v 1 , C v 2 ]. Therefore, we can use the given information if we take v 1 = ± 1 2 ² and v 2 = ± 2 1 ² , 21 /september/ 2005; 22:09 40...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
 Fall '08
 Gladue
 Calculus, Multiplication

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