Name_______________________________________________ Date _____________ Period Discrete Math Chapter 2 Final Exam Review Solve the system. Perform the indicated operation. 1) 6x - 7y = 54 7) -5 1 + 6 2 2x - 4y = 18 25 52 A) (9, 1) B) (9, 0) 3 4 A) C) No solution D) (8, 1) 37 C) 1 3 77 Use the echelon method to solve the system. 2) 3x + 5y + z = -24 5x - 4y - z = -2 4x + y + 2z = -24 A) (-5, -2, -3) C) No solution
8) B) (-3, -5, -2) D) (-3, -2, -5)
Solve the problem. 3) Carole's car averages 14.6 miles per gallon in city driving and 25.3 miles per gallon in highway driving. If she drove a total of 666.6 miles on 31 gallons of gas, how many of the gallons were used for city driving? A) 11 gallons B) 20 gallons C) 13 gallons D) 25 gallons
21 - 74 22 3 -3 A) 7 0 -6 6 1 5 C) 7 8 10 -1
B) 18 D) 1 -3 0 -3
-1 4 0 4 8 -4
-3 3 B) -7 0 6 -6 1 3 D) 7 0 6 -2
Find the indicated matrix product, if possible. 9) A = 1 0 , B = 1 2 -2 . Find AB. 03 2 -2 2 A) AB is not defined. B) 1 0 0 0 -6 6 C) 6 -6 6 1 2 -2 D) 1 2 -2 6 -6 6
Write an augmented matrix for the system of equations. 4) 3x + 8y = 34 -2x + 6y = 34 A) 34 8 3 B) 3 8 34 34 -2 6 6 -2 34 3 8 34 C) D) 3 -2 34 8 6 34 -2 6 34
Find the inverse of the matrix. 10) A = -4 -2 6 0 A) 1 1 3 6
Use the Gauss-Jordan method to solve the system of equations. 5) 4x + 2y = -10 3x + 6y = 15 A) (5, -5) B) No solution C) (-5, 5) D) (-5, -5)
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Find the values of the variables in the matrix. 6) -9 3 = x y 8 9 8z A) x = 3, y = -9, z = 9 B) x = -9, y = 3, z = 9 C) x = -9, y = 3, z = 8 D) x = -9, y = 8, z = 9
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1 0 2
1 1 2 3 1 6
0
C)
D) 0 -
1
B)
1 6
1 1 2 3
0 -
1 6
1 1 2 3
