MATH 204 Exam 2, Fall 2005

Time: 1 hour Math 204 Date: October Quiz 1 First Semester 05/06 Instructor: Mrs. Muna Jurdak Section 9 Tues. 3:30 Section 10 = Tues. 2:00 Section 11 Tues. 12:30 Section 12 Tues. 11:00. Instructions: 1. Write your name and ID number clearly where indicated. 2. Circle your section number above, according to the time of the problem solving session in which you are enrolled. 3 Solve the problems on this, the white question sheet. Use the colored sheets for scratch work only. You may use the back of a white sheet to complete the solution of a problem. Problem 1 /10 Problem 2 /20 Problem 3 ‘10 Probiem 4 AWS Problem 5 ‘10 Problem 6 /20 Problem 7 AS Total /100 (10%) 1. Given the matrices, 1 4 2 1 1 6 A=|_ , C= 10 2), De 1 5 -3 1 301 Perform the following operations, if possible. (a) A+2B (b) AC (c) CB (d) C"D. 20%) 2. (a) Using the cofactor method, find the inverseofthe matrix A, 4 2 A=|2 0}. 1 3 (b) Write the following system of equations in matrix form. Then solve the system using matrices. 4x). + X27 +2x3=0 2x, +5x2 =]2 X1 +2x) +3x3= 4 (10%) 3.Using the Gaussian procedure, find the inverse of the following matrix A, if the inverse exists. 2 -3 -7 Wi (15%) 4. A game consists of flipping a coin followed by rolling a die. Let A = the event of getting a head and then an even number on the die. B = the event of getting a head and then an odd number on the die. C = the event of getting a tai] and then a number 4 or more on the die. D = the event of getting a tail and then a number 5 or less on the die. (a) Find the following probabilities: p(A’), p(C), p(D), and p(C UD). (b) Are the events A, B,C,D (i) Mutually exclusive? (ii) Collectively exhaustive? Give reasons for your answers for part (b). (10%) 5. A box contains 7 red marbles and 4 white marbles. Three marbles are drawn from the box one after the other (without replacement). Find the probability that the first 2 are red and the third is white. (20%) 6. Seven squares, 4 red, 3 green, are to be arranged in a row. Find the number of ways that this can be done: (a) if there are no restrictions (b) if squares of the same color must be next to each other. (c) If the green squares only must be next to each other. 1 (15%)7. (a) A woman has 12 close friends. Find the number of ways that she can invite 5 of them to dinner. (b) If two of the woman's friends are married and will not attend separately, find the number of ways that the woman can invite 5 of her 12 friends.