Solve the system of equations. 1) 1) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Assignment Ch Name Solve the system of equations. ) ) x y z = - x - y z = x y z = x = -, y = -, z = ; (-, -, ) x =, y = -, z = -; (, -, -) x = -, y =, z = -; (-,, -) inconsistent ) The perimeter of a parking lot is 00 yards. Find the dimensions of the lot if the length is 0 ) yards more than three times the width. Solve the system of equations by substitution. ) ) x 7y = - x y = x = 7, y = ; (7, ) x =, y = 7; (, 7) x =, y = -; (, -) x = -, y = ; (-, ) Verify that the values of the variables listed are solutions of the system of equations. ) ) x y z = - x - y z = - x y z = 9 x = -, y = -, z = solution not a solution Solve the system of equations by substitution. ) ) x y = x = -8 x = -, y = -; (-, -) x =, y = -; (, -) x = -, y = ; (-, ) x = -, y = 0; (-, 0)

2 Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 6) 6) x - y = 7 x y = x =, y = -;, - x = 6, y = - ; 6, - x =, y = ;, inconsistent 7) 7) -x y = 7 x - y z - w = z w = x = - - 6w, y = w, z = - w, where w is any real number or (x, y, z, w) x = - - 6w, y = w, z = - w, where w is any real number x = w, y = - - 6w, z = - w, where w is any real number or (x, y, z, w) x = w, y = - - 6w, z = - w, where w is any real number x = - 0 w, y = - 6w, z = - w, where w is any real number or (x, y, z, w) x = - 0 w, y = - 6w, z = - w, where w is any real number inconsistent 8) The perimeter of a picture frame is feet. If three times the height is equal to eight times 8) the width, what are the dimensions of the frame? Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 9) 9) x y = 8 y = x = -, y = ; (-, ) x = -, y = -; (-, -) x =, y = -; (, -) inconsistent 0) 0) 9x 7y - z = 7 x 8y 8z = 67 -x y z = - x =, y = 7, z = ; (, 7, ) x = -, y =, z = 6; (-,, 6) x =, y =, z = 7; (,, 7) inconsistent

3 Find the value of the determinant. ) ) Use properties of determinants to find the value of the second determinant, if the value of the first is known. ) ) x y z - u v w = -8 u v w =? - x y z cannot be determined ) Determinants are used to show that three points lie on the same line (are collinear). If ) x y x y x y = 0, then the points (x, y), (x, y), and (x, y) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (6, 0), (0, ), and (8, ) collinear? Yes No Solve the system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. ) ) x y = y = x = -, y = ; (-, ) x =, y = ; (, ) x =, y = ; (, ) x = -, y = -; (-, -) ) ) y = 0 x - y = -6 x =, y = 8;, 8 x =, y = 0 ;, 0 x = -, y = 6 ; -, 6 not applicable Use the given matrices to compute the given expression. 6) If A = - and B = -, find -A B. 6)

4 Encode or decode the given message, as requested, numbering the letters of the alphabet through 6 in their usual order. 7) Use the coding matrix A = 7 to encode the message LIFE. 7) ) State University has a College of Arts & Sciences, a College of Business, and a College of 8) Engineering. The percentage of students in each category are given by the following matrix. Arts & Sciences Business Engineering Freshman Sophomore Junior Senior 60% 0% 0% 70% 0% 0% 0% 0% 0% 0% 0% 0% The student population is distributed by class and age as given in the following matrix. Freshman Sophomore Junior Senior Female Male How many female students are in the College of Business? How many male students are in the College of Arts & Sciences? 7 students; 70 students students; 69 students 70 students; 7 students 69 students; 9 students 9) The matrix 9 represents one week's usage of wood (in board-feet) at two locations of a 9) company that manufactures chairs. Due to differences in transportation costs, the first location pays $0.89 per board-foot and the second location pays $0.9 per board-foot. (a) Find a by matrix representing the cost of the wood. (b) Multiply the given matrix and the matrix found in part a to determine the total cost of wood for that week. Use the given matrices to compute the given expression. 0) Let C = - and D = - -. Find C - D. 0)

5 Write the partial fraction decomposition of the rational expression. x ) (x - )() x - (x - ) - (x - ) - x - - x - (x - ) x - - (x - ) ) ) x x (x ) ) x 0x x (x ) x 0x - x (x ) x - -0x x (x ) x -0x - x (x ) ) x - x x - x - (x - ) x - x - 9 (x - ) x x - - (x - ) x - x - (x - ) ) Tell whether the given rational expression is proper or improper. ) x - x 8 x - 9x 0 ) Improper Proper Write the partial fraction decomposition of the rational expression. ) x - 6 x x - 6 x - x - x x x - x 9 x - x - - x 9 x - x - x 9 )