2/3/2016 NS116 Unit 5b Assignment Mandie AdlerMOL NS116 (6 Week), section XM1A, Winter 2016 Instructor: Linda Desjardines WebAssign NS116 Unit 5b Assignment (Homework) Current Score : - / 20 Due : Sunday, February 7 2016 11:59 PM CST 1. -/1.53 pointsAufColAlg8 7.1.001. Write the augmented matrix, the coefficient matrix, and the constant matrix of the system of equations. 4x 2y + z = 17 5x 3y + 4z = 25 x + 3z = 6 augmented matrix coefficient matrix constant matrix http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 1/8 2/3/2016 NS116 Unit 5b Assignment 2. -/1.53 pointsAufColAlg8 7.1.004. Write the augmented matrix, the coefficient matrix, and the constant matrix of the system of equations. x y + 2z + 4w = 5 5x + z 5w = 1 4x 5w = 1 x + 5y z = 8 augmented matrix coefficient matrix constant matrix 3. -/1.53 pointsAufColAlg8 7.1.014. Use elementary row operations to write the matrix in row echelon form. 1 2 4 1 2 2 7 3 3 6 8 1 http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 2/8 2/3/2016 NS116 Unit 5b Assignment 4. -/1.53 pointsAufColAlg8 7.1.021. Solve the system of equations by the Gaussian elimination method. (If the system is dependent, enter a general solution in terms of c1, c2, . If there is no solution, enter NO SOLUTION.) x + 5y = 31 4x + 3y = 22 (x, y) = 5. -/1.53 pointsAufColAlg8 7.1.027. Solve the system of equations by the Gaussian elimination method. (If the system is dependent, enter a general solution in terms of c. If there is no solution, enter NO SOLUTION.) 3x + 7y 7z = 7 x + 2y 3z = 2 5x + 6y + z = 30 (x, y, z) = 6. -/1.53 pointsAufColAlg8 7.1.059. Find an equation of the plane that passes through the points (1, 0, 4), (2, 1, 2), and (1, 1, 1). (Suggestion: The equation of a plane can be written as z = ax + by + c.) z = http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 3/8 2/3/2016 NS116 Unit 5b Assignment 7. -/1.53 pointsAufColAlg8 7.2.007. Consider the following. A = 2 1 1 2 B = 2 2 2 1 (a) Find A + B. (b) Find A B. (c) Find 2B. (d) Find 2A 3B. http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 4/8 2/3/2016 NS116 Unit 5b Assignment 8. -/1.53 pointsAufColAlg8 7.2.013.MI. Consider the following. 2 A = 3 1 0 1 4 3 3 4 2 2 B = 2 3 1 3 3 1 2 (a) Find A + B. (b) Find A B. (c) Find 2B. (d) Find 2A 3B. http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 5/8 2/3/2016 NS116 Unit 5b Assignment 9. -/1.53 pointsAufColAlg8 7.2.015. Find AB and BA, if possible. (If not possible, enter IMPOSSIBLE in any single blank.) A = 3 2 3 3 B = 1 3 3 2 AB = BA = 10.-/1.53 pointsAufColAlg8 7.2.023. Find AB, if possible. (If not possible, enter IMPOSSIBLE in any single blank.) 1 0 A = [ 1 5 4 ] and B = 5 1 1 5 AB = 11.-/1.53 pointsAufColAlg8 7.2.025. Find AB, if possible. (If not possible, enter IMPOSSIBLE in any single blank.) A = 1 5 2 3 1 2 B = 3 1 0 2 AB = http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 6/8 2/3/2016 NS116 Unit 5b Assignment 12.-/1.53 pointsAufColAlg8 7.2.039. Biologists use capturerecapture models to estimate how many animals live in a certain area. A sample of fish are caught and tagged. When subsequent samples of fish are caught, a biologist can use a capture history matrix to record (with a 1) which, if any, of the fish in the original sample have been caught again. The rows of this matrix represent the particular fish (each has its own identification number), and the columns represent the number of the sample in which the fish was caught. Here is a small capture history matrix. Sample 1 2 3 4 Fish A 1 0 0 1 Fish B 0 1 1 1 Fish C 0 0 1 1 (a) What is the dimension of this matrix? Write a sentence that explains the meaning of dimension in this case. Select different fish were caught in Select different samples. (b) What is the meaning of the 1 in row A, column 4? Fish C was caught in sample 1. Fish C was not caught in sample 1. Fish A was not caught in sample 4. Fish A was caught in sample 4. Fish B was caught in sample 2 (c) Which fish was captured the most times? Fish A Fish B Fish C http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 7/8 2/3/2016 NS116 Unit 5b Assignment 13.-/1.64 pointsAufColAlg8 7.2.040. Biologists can use a predatorprey matrix to study the relationships among animals in an ecosystem. Each row and each column represents an animal in the system. A 1 as an element in the matrix indicates that the animal represented by that row preys on the animal represented by that column. A 0 indicates that the animal in that row does not prey on the animal in that column. A simple predatorprey matrix is shown below. The abbreviations are H = hawk, R = rabbit, S = snake, and C = coyote. H R S C H R S C 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 (a) What is the dimension of this matrix? Write a sentence that explains the meaning of dimension in this case. There are Select different animals in this system. (b) What is the meaning of the 0 in row R, column H? Rabbits do not prey on hawks. Rabbits do not prey on other rabbits. Rabbits do not prey on snakes. Rabbits do not prey on coyotes. (c) What is the meaning of there being all zeros in column C? The Select is not preyed on by any other animal in this system. (d) What is the meaning of all zeros in row R? The Select does not prey on any animal in this system. http://www.webassign.net/web/Student/AssignmentResponses/last?dep=12914386 8/8