Section 3.7 Solving Systems of Linear Equations by Using Matrices 301 29. Given the matrix M M c 1 3 5 4 ` 2 1 d write the matrix obtained by multiplying the first row by 3 and adding the result to row 2. 30. Given the matrix N N c 1 2 3 2 ` 5 12 d write the matrix obtained by multiplying the first row by 2 and adding the result to row 2. 31. Given the matrix R R £ 1 3 0 4 1 5 2 0 3 † 1 6 10 § a. Write the matrix obtained by multiplying the first row by 4 and adding the result to row 2. b. Using the matrix obtained from part (a), write the matrix obtained by multiplying the first row by 2 and adding the result to row 3. 32. Given the matrix S S £ 1 2 0 5 1 4 3 4 5 † 10 3 2 § a. Write the matrix obtained by multiplying the 5 first row by and adding the result to row 2. b. Using the matrix obtained from part (a), write the matrix obtained by multiplying the first row by 3 and adding the result to row 3. For Exercises 33–36, use the augmented matrices A, B, C, and D to answer true or false. c 1 23 5 2 C D c d 12 8 A d c 6 4 c 5 2 B d 5 2 ` 13 7 6 4 ` 7 2 5 2 ` 2 7 d 33. The matrix A is a 2 3 matrix. 34. Matrix B is equivalent to matrix A. 35. Matrix A is equivalent to matrix C. 36. Matrix B is equivalent to matrix D. ` 7 4 37. What does the notation mean when 38. What does the notation mean when R23R1 2R3 1 R3 one is performing the Gauss-Jordan method? one is performing the Gauss-Jordan method? 39. What does the notation 40. What does the notation mean 3R1 R2 1 R2 4R2 R31 R3 mean when one is performing the Gauss- when one is performing the Gauss-Jordan Jordan method? method? For Exercises 41–56, solve the system by using the Gauss-Jordan method. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. (See Example 4–7.) 41. x 2y 1 42. x 3y 3 43. x 3y 6 44. 2x 3y 2 2x y 7 2x 5y 4 4x 9y 3 x 2y 13 45. 46. 47. 48. x 3y 3 2x 5y 1 x y 4 2x y 0 4x 12y 12 4x 10y 2 2x y 5 x y 3 49. 50. 51. 52. x 3y 1 x y 4 3x y 4 2x y 4 3x 6y 12 2x 4y 4 6x 2y 3 6x 3y 1 53. 54. 55. 56. x y z 6 2x 3y 2z 11 x 2y 5 z 5x 10z 15 x y z 2 x 3y 8z 1 2x 6y 3z 10 x y 6z 23 x y z 0 3x y 14z 2 3x y 2z 5 x 3y 12z 13
miller_intermediate_algebra_4e_ch1_3
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