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MTH: 160 COLLEGE ALGEBRA CHAPTER 6 Review NAME_________________________ Please show all your work on this test and place your final answers in the provided spaces. Thank you and good luck. 1) (19 PTS) Solve systems by methods described. If any solutions are infinitely many give the generic solution. a) Solve the system graphically. Ans:__________________ Use calculator and show graph. 2x y 2 4 x 3 y 24 1 b) Solve by substitution method. Ans:__________________ 4x y 2 2 y 8 x 4 c) Solve by elimination method. Ans:_______________________ 2x 6y 7 1 10 xy 3 9 2 2) (15 PTS) Given m 2n t 1 2m t 1 m n 1 Solve the system using Gauss elimination and backwards substitution. Please provide the matrix solution from your grapher. Rewrite the matrix solution with coefficients and variables before doing backwards substitution. Convert all answers to improper fractions. Solve the system using Gauss-Jordan Elimination (rref). Please provide the matrix solution from your grapher. 3 3) (6 PTS) Given the matrix equation, AX B, solve for X. Please show all supporting steps! 4) (9 PTS) Given 3 x 3 y 2z 4 x 3 y z 10 5 x 2y 3z 8 a) Write an equivalent matrix equation AX B. b) Use a grapher to solve the system. X 5) (5 PTS) Given x 8 3 21 2y 1 6 2 3 5 = 8 3 z 7 21 9 6 2 5 , Find x, y & z 12 Ans:___________________________ 4 6) (24 PTS) Matrix Operations 9 0 4 6 a) Given A and B , Find A B -3 6 7 8 4 8 3 1 5 b) Given A and B 1 1 , Find AB -2 0 6 0 3 1 1 7) (10 pts) Given A 2 3 1 1 2 1 'evaluate the determinant 3 A using the "Hot Dog" method. Ans:_____________________________ 5 8) A 3-oz serving of roasted, skinless chicken breast contains 140 Cal, 27 g of protein, 3 g of fat, 13 mg of calcium, and 64 mg of sodium. One-half cup of potato salad contains 180 Cal, 4 g of protein, 11 g of fat, 24 mg of calcium, and 662 mg of sodium. One broccoli spear contains 50 Cal, 5 g of protein, 1 g of fat, 82 mg of calcium, and 20 mg of sodium. a) Write 1 X 5 matrices C, P, and B that represent the nutritional values of each food. b) Find C + 2P + 3B and tell what the entries represent. 6 9) Analyze the different solutions you can get when solving a 3 X 3 matrix on the grapher. Please write your matrix before and after solving. State whether the results from the grapher denote one solution, no solution or infinitely many solutions and the reason for you conclusion. mnt 9 m n t 15 3m n t 2 2 x 3 y 2z 2 x 4y z 9 3 x y 5z 5 p q r 1 p 2q 3r 4 4 p 5q 6r 7 7 10) The total volume of passenger traffic by private automobile, by bus (excluding school buses and urban transit buses), and by railroads in the United States in a recent year was 1899 billion passenger-miles. (One passenger-mile is the transportation of one passenger the distance of one mile.) The volume of bus traffic was 21 billion passenger-miles more than the volume of railroad traffic. The total volume of bus traffic was 1815 billion passenger-miles less than the volume of traffic by private automobile. What was the volume of each type of passenger traffic? 8