review3 - Math 375 Review problems III Do the following...

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Math 375 – Review problems III Do the following problems from the book. 3.6: 4a, c, 6. 3.11: 5. 3.17: 1c, 2c, 3c. 4.4: 2, 5. 4.8: 4, 5, 6, 8, 11. Review the handout on determinants to do No. 9 in 4.8. or come up with your own proof. 5.11: No 1, 5, 7, 8, 12. 1. Let A = 2 - 1 0 5 0 0 2 0 0 3 7 4 1 2 5 3 . Evaluate the determinant of A . b) Is A invertible? If so compute the determinants of ( A t ) - 1 and A 5 (do not compute A 5 ). c) Let x R 4 be the solution of 2 - 1 0 5 0 0 2 0 0 3 7 4 1 2 5 3 x 1 x 2 x 3 x 4 = 2 0 - 6 - 4 Determine the coordinate x 3 without using Gaussian elimination and without com- puting the inverse A - 1 . 2. i) Find the 2 × 2 matrix A = ± a b c d ² which satisfies A ± 2 3 ² = ± 8 12 ² , A ± 1 1 ² = ± 1 1 ² . (ii) Find A 1000 . 3. Let u 1 = 1 1 1 , u 2 = 0 - 1 1 , u 3 = 2 - 1 - 1 . Find the 3 × 3 matrix A which satisfies Au 1 = 2 u 1 , Au 2 = 4 u 2 , Au 3 = 3 u 3 . (Observe that the
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review3 - Math 375 Review problems III Do the following...

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