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# sol-a1 - 0 3 1 4 2 4 0 4 3 2 1 ⊗ 0 1 2 3 4 5 0 0 0 0 0 0...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Programming and Optimazation MATB61 Winter 2008 Addition: 1. Z 5 Z 6 0 1 2 3 4 0 0 1 2 3 4 1 1 2 3 4 0 2 2 3 4 0 1 3 3 4 0 1 2 4 4 0 1 2 3 0 1 2 3 4 5 0 0 1 2 3 4 5 1 1 2 3 4 5 0 2 2 3 4 5 0 1 3 3 4 5 0 1 2 4 4 5 0 1 2 3 5 5 0 1 2 3 4 0 1 2 3 4 0 0 0 0 0 0 1 0 1 2 3 4 2 0 2 4 1 3 3

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Unformatted text preview: 0 3 1 4 2 4 0 4 3 2 1 ⊗ 0 1 2 3 4 5 0 0 0 0 0 0 0 1 0 1 2 3 4 5 2 0 2 4 0 2 4 3 0 3 0 3 0 3 4 0 4 2 2 4 2 5 0 5 4 3 4 1 There are no multiplicative inverses for 2, 3, 4. 2. Yes, U is a field under the indicated operations. 3. Yes, the matrix is invertible in Z 7. Since det(A) = 15 – 24 = - 9 = 5 But it isn’t invertible in Z 9 . Fraleigh & Beauregard , Pages189-190 1...
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sol-a1 - 0 3 1 4 2 4 0 4 3 2 1 ⊗ 0 1 2 3 4 5 0 0 0 0 0 0...

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