Unformatted text preview: Problems: 1. Fraleigh & Beauregard , Pages189190 # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 19, 22, 23, 24, 25. 2. Addition: 1) Show that Z 5 is a field. Show that Z 6 is not a field. 2) 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 + + + . 3) Is the matrix A = over Z 7 invertible? ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 3 4 6 5 Note: There are answers at the back of the textbook for the odd number questions....
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 Spring '10
 X.Jiang
 Linear Algebra, Algebra, Vector Space, Fraleigh

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