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Unformatted text preview: c) 1 1 3 1 2 1 1 2 2 3 2 2 2 1 3 2 1 1 1 1 1 n n n n n n n x x x x x x x x x x x x 2) Discuss the constants a , b , c so that the following system has trivial solution 2 2 2 z c cy x z b by x z a ay x 3) Show that Z 7 is a field. Show that Z 6 is not a field. 4) Determine if that U = { 3 b a  a , b Q} is a field under the operations and , where is given by ( 3 b a ) ( 3 d c ) = 3 ) ( ) ( d b c a and is given by ( 3 b a ) ( 3 d c ) = 3 ) ( ) 3 ( bc ad bd ac . 5) Is the matrix A = 3 4 6 5 over Z 7 invertible? Where isn’t A invertible over? Note: There are answers at the back of the textbook for the odd number questions....
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 Fall '09
 Yiang
 Linear Algebra, Algebra, Fraleigh

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