Exercise Set 3.2: Solving Systems of Linear Equations Using Matrices Determine whether each of the given augmented matrices is in row reduced form. If not, state the condition or conditions that have been violated. 10. 1 0 0 1 0 0 0 0 0 1 4 8 1. 1 0 0 0 1 3 11. 1 0 3 6 0 1 5 10 2. 1 2 0 0 0 0 12. 1 1 11 17 0 1 0 2 3. 1 1 6 0 1 4 13. 1 0 1 6 13 0 0 1 0 21 4. 2 0 9 0 1 1 14. 1 0 0 2 2 0 0 1 3 8 5. 1 3 10 0 0 0 0 0 0 6. 1 2 15 0 1 5 0 0 0 7. 8. 9. Each of the matrices below are in row reduced form. Give the solution set for the associated system of linear equations. 15. 1 0 32 0 1 2 1 0 6 0 0 1 4 2 0 0 3 3 16. 1 0 0 1 0 1 0 3 0 0 1 10 1 0 5 2 0 1 3 7 0 0 0 0 17. 1 2 15 0 0 16 0 0 0 1 0 0 1 0 1 0 2 0 0 1 3 18. 1 0 0 0 0 1 5 5 0 0 0 1 19. 1 0 2 1 0 1 2 1 MATH 1313 Finite Mathematics with Applications 151 Exercise Set 3.2: Solving Systems of Linear Equations Using Matrices 20. 1 0 0 8 10 0 1 1 14 21 Use the Gauss-Jordan Elimination Method to solve each of the following systems of equations. 21. 30. 2 x 3 y = 13 x + 2 y = 8 4 x y = 5 31. 3 x + 5 y = 10 x 2y =1 7 x 14 y = 14 32. 3 x + 9 y = 12 x 3 y = 4 2x + 6 y = 8 2 x + 3 y = 8 x y =2 22. 3 x 9 y = 27 4x 2 y = 6 23. 6 x 6 y = 14 x + y =1 33. x 3 y + 6 z 13w = 0 x + 5 y 10 z + 21w = 2 24. x + 4y =1 3 x + 12 y = 0 34. 2 x + 6 y + 18 z = 8 2 x + 7 y + 20 z = 9 25. 5 x 4 y = 12 10 x + 8 y = 24 35. 3 x + 18 y 21z = 24 2 x + 12 y 14 z = 26 26. 2 x + 6 y = 32 x 3 y = 16 36. x 2 y z + 4w = 5 x + 2 y + z 4 w = 11 27. 3 x + 4 y = 12 x y = 4 2x 3y = 8 37. 4x + 2 y + 2z = 0 x + y z =1 3x + y + z = 5 28. 2x 4 y = 3 5 x + 2 y = 10 6 x + 12 y = 6 38. x y + z = 5 4 x + 2 y 2 z = 8 6 x + 3 y 10 z = 5 39. 29. x + 4 y = 20 1 x 2 y = 10 2 3 x + 12 y = 60 2 x + y 2z = 2 x y + 3z = 0 10 x + 5 y 10 z = 10 152 University of Houston Department of Mathematics Exercise Set 3.2: Solving Systems of Linear Equations Using Matrices 40. 2 x + 4 y + 6 z = 20 3 x 2 y + 4 z = 22 6 y 2z = 8 41. 2x 9 y = 0 x + 5 y z = 3 x+ y+z=3 42. 4x + y = 5 x + 2y + z = 2 3 x 6 y 3 z = 6 MATH 1313 Finite Mathematics with Applications 153 Math 1313 Homework 5 Section 3.2 1. The choices for problem number 6 from the book are given below. a. Row Reduced b. Not Row Reduced 2. The choices for problem number 8 from the book are given below. a. Row Reduced b. Not Row Reduced 3. The choices for problem number 12 from the book are given below. a. Row Reduced b. Not Row Reduced Use the following matrices for questions 4-6. 1 0 2 0 1 0 , 0 0 0 1 0 0 1 0 0 3 2 , 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 5 , 3 0 3 7 4. State the number of solutions for Matrix A. a. No Solution b. One Solution c. Infinitely Many Solutions 5. State the number of solutions for Matrix B. a. No Solution b. One Solution c. Infinitely Many Solutions 6. State the number of solutions for Matrix D. a. No Solution b. One Solution c. Infinitely Many Solutions 7. Solve the following system of linear equations using the Gauss-Jordan elimination method for the variable x. 3 6 0 6 10 4 a. No Solution b. 4 c. 3 d. 3 1 Math 1313 Homework 5 Section 3.2 e. 2 8. Solve the following system of linear equations using the Gauss-Jordan elimination method for the variable y 2 10 5 2 2 3 0 10 10 a. No\tSolution b. 2/3 , where\tz\tis\tany\treal\tnumber c. d. e. , where\tz\tis\tany\treal\tnumber 2 , where\tz\tis\tany\treal\tnumber 9. Solve the following system of linear equations using the Gauss-Jordan elimination method for the variable x. 1 3 2 0 2 4 a. No Solution b. 2 c. 3 d. , where\ty\tis\tany\treal\tnumber e. 2 10. Solve the following system of linear equations using the Gauss-Jordan elimination method for the variable x. 4 1 2 7 1 5 3 1 a. 6 b. 2 c. 2 d. 1 e. No Solution 2