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Math 1050-1 Homework Set 10 I just talked with the person in change of posting the homework sets, and he won’t be able to get this set posted until Thursday. I have written out the problems for you so you can start on them and then enter them once the set is posted. 1. Give the partial fraction decomposition of 4x2 − 35x + 34 . x3 − 3x2 − 10x + 24 Note: x3 − 3x2 − 10x + 24 = (x − 2)(x + 3)(x − 4). 2. Give the partial fraction decomposition of 7x + 2 . +x−2 x2 3. Give the partial fraction decomposition of x2 7x − 29 . + 2x − 15 4. Give the partial fraction decomposition of 7x − 19 . x2 − 6x + 9 5. Give the partial fraction decomposition of 3x2 − 3x + 8 . x3 + 4x 6. Solve the following system: x+y+z = 10 (1) 2x − y + 3z 3x + y − 4z = 9 = 15 (2) (3) 7. Solve the following system: r+s+t+u = r + 2s + 3t + 4u = −7 −28 (4) (5) r − s + 2t − u = −3 (6) r + 2s − 3t + 2u = 12 (7) 8. Let p be the quartic (degree 4) polynomial that satisfies p(i) = 2i , i = 0, 1, 2, 3, 4. What is p(x)? 9. For the following linear systems, you will need to enter ”U” if the system has a unique soltuion, ”N” if it has no solution, and ”I” if it has infinitely many solutions. (a) 3x + 4y = 1 3x − 4y = 1 3x + 4y 6x + 8y = 1 = 1 (b) (c) 3x + 4y = 1 6x + 8y = 2 10. You have boxes of five types. They are characterized by their length L, their width W , their height H, their age A, and their price P , as given in the following table: type I II III IV V So for 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. L W 1 1 1 1 1 2 1 2 1 2 example, H A P 1 1 1 2 3 2 3 2 2 4 1 2 5 1 3 boxes of type IV measure 1 by 2 by 4 feet, are one year old, and cost $2 each. Suppose the sum of the lengths of your boxes is 20, the sum of their widths 28, the sum of their heights 46, the sum of their ages 32, and the total price of those boxes 34. How many of each type of boxes do you have? 0 −6 −8 3 Let A = and B = . Then what is AB? −1 −2 3 8 8 −2 −3 0 Let A = and B = . Then what is AB? −1 −4 8 −9 3 −6 −6 −4 Let A = and B = . Then what is AB? −5 4 1 −2 0 −6 1 −5 Let A = and B = . Then what is AB? −2 −5 −8 4 0 3 3 5 Let A = and B = . Then what is AB − BA? 2 2 7 0 7 −3 −7 −6 8 Let A = and B = 3 8 . Then what is AB? What is BA? 4 −8 −7 1 4 1 2 −3 −2 Let A = and B = . Then what is 3A − 2B? 2 1 4 2 2 1 1 2 −3 4 Let A = and B = . Then what is 3A − 2B? −1 −1 4 −3 1 −2 1 0 3 −2 1 6 Let A = and B = . Then if possible, what is AB? What is the order of 6 13 8 −17 4 2 AB? −1 3 1 2 Let A = 4 −5 and B = . Then if possible, what is AB? What is the order of AB? 0 7 0 2