aspenfields 2 years ago how do i solve the system of equations? 2x + 4y + 3z = 6 3x + 5y + 6z =3 2x + 3y + 4z = 8

1. beketso

are you familiar with matrices

2. aspenfields

kinda

3. beketso

well you can use the gaussian elimination

4. aspenfields

ok

5. beketso

meaning you use the elementary row operations

6. aspenfields

yea

7. beketso

2 4 3 | 6 3 5 6 | 3 2 3 4 | 8 subtract row 1 from row 3 and tell me what u get

8. aspenfields

ok one sec

9. aspenfields

0 -1 1 |2 is that right?

10. beketso

yeah.now divide row 1 by 2

11. aspenfields

ok the answer i have above isnt row one is it or is row one in the problem still?

12. beketso

no.it is still row 3.row one is ur original problem 2 4 3 | 6

13. aspenfields

ok

14. aspenfields

2/3 4/5 1/2 |2 right?

15. beketso

it is actually 1 2 3/2 | 3 get it?

16. aspenfields

how?

17. beketso

well u take the first row.and u divide by 2.then it changes from 2 4 3 |6 to 1 2 3/2 | 3

18. aspenfields

ohh! u divid by two not thr 2nd row :/lol now i got that ok

19. beketso

then your rows are now like this 1 2 3/2 | 3 3 5 6 | 3 0 -1 1 | 2

20. aspenfields

yea

21. beketso

sorry. multipy row 1 by 3 the subtract it from row 2 the u have a reduced row 2

22. aspenfields

ok? one sec

23. aspenfields

when i subtract which number should be on top?

24. beketso

1 2 3/2 | 3 _ _ _ | _ 0 -1 1 | 2 the only r0w that changes is row 2

25. aspenfields

yea,ok i get that so row to is now 3 8 9/2 |-3

26. beketso

3-(3X3) = 0 That is how u do it.

27. aspenfields

what?

28. beketso

meaning u take 1 from row1 and multiply by 3 the u subtract the answer from 3 in row 2 and u get ur as 0. do the same with the second term

29. beketso

then u get 1 2 3/2 | 3 0 -1 3/2 | -6 0 -1 1 | 2

30. aspenfields

ohh

31. aspenfields

ok then from there what do i do next ?

32. beketso

multiply row 2 by -1

33. aspenfields

ok

34. aspenfields

0 1 -3/2 |6

35. beketso

exactly

36. aspenfields

ok is this the answer or is the more?

37. beketso

1 2 3/2 | 3 0 1 -3/2 | 6 0 -1 1 |2 in row 1 u must eliminate 2 and in row 3 must eliminate -1.

38. aspenfields

why?

39. beketso

add row 3 and row 2 to get 1 2 3/2 |3 0 1 -3/2 |6 0 0 1/2 |-4 and u jst eliminated 1 from row 3

40. aspenfields

ok

41. beketso

sorry u jst eliminated -1 from row 3

42. beketso

then now we eliminate 2 from row 1

43. aspenfields

i figured u ment that

44. aspenfields

:)

45. beketso

do this row1-2(row2)

46. beketso

then u get 1 0 9/2 |-9 0 1 -3/2 | 6 0 0 1/2 |-4

47. beketso

getting this?

48. aspenfields

yea

49. beketso

basically u want to get to a point were u have 1 0 0 | ? 0 1 0 | ? 0 0 1 | ?

50. beketso

now divide row 3 by 1/2 (half)

51. aspenfields

ohh ok

52. aspenfields

1 |-2

53. beketso

what is 4 divided by half

54. aspenfields

oh 8

55. beketso

then u have 1 0 9/2 | -9 0 1 -3/2 | 6 0 0 1 | -8 what do u think u should do to eliminate 9/2?

56. aspenfields

2/9?

57. beketso

58. aspenfields

u mulitply?

59. beketso

remember you want it to be 0

60. aspenfields

on then subtract 9/2?

61. beketso

exactly

62. aspenfields

ok :)

63. aspenfields

what bout the numbers on the end?

64. beketso

so mentally multiply row 3 by 9/2

65. beketso

and then subtract it from row 1

66. beketso

what do u get for row1?

67. aspenfields

1 0 0 |1?

68. beketso

actually 1 0 0 |27

69. aspenfields

oh

70. beketso

now u got 1 0 0 | 27 0 1 -3/2 |6 0 0 1 |-8

71. beketso

u must now eliminate -3/2.how do u think u do that?

72. aspenfields

yes

73. beketso

how do you think u can do it?

74. aspenfields

plus 3/2

75. beketso

sure.which row can u use to eliminate it?

76. aspenfields

3

77. beketso

good.how do u do that?

78. aspenfields

idk

79. beketso

multiply row3 by 3/2 and add it to row2

80. aspenfields

ok

81. beketso

that way 1 becomes 3/2 and you can add that to row 2.the -3/2 + 3/2 = 0 which eliminates 3/2

82. aspenfields

yea

83. beketso

then u have 1 0 0 |27 0 1 0 |-6 0 0 1 |-8 what is ur x,y and z?

84. aspenfields

27,-6,-8?

85. beketso

yes

86. aspenfields

ok

87. beketso

but i think i made a mistake with the numbers somewhere

88. beketso

should i paste the whole solution or can u figure out the mistake?

89. aspenfields

i can figure it out now

90. beketso

ok.sure