## UsukiDoll Group Title solve the system of linear equations using the Gauss–Jordan elimination method. 2x-3y=8 4x+y=-2 one year ago one year ago

1. UsukiDoll Group Title

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2. UsukiDoll Group Title

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3. UsukiDoll Group Title

ugh I missed that one on my paper! that subtraction because -16-(-2) is - 14

4. UsukiDoll Group Title

anyway|dw:1361067211535:dw|

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6. UsukiDoll Group Title

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7. Callisto Group Title

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8. UsukiDoll Group Title

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9. Callisto Group Title

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10. UsukiDoll Group Title

I'm using elementary row operations.

11. UsukiDoll Group Title

oh crud

12. UsukiDoll Group Title

spotted anotehr error. not my day today

13. UsukiDoll Group Title

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14. UsukiDoll Group Title

arghhh...

15. UsukiDoll Group Title

ok really...I put this in reduced row echleon form. got my solution, but geez doesn't even equal back into the equation

16. Callisto Group Title

Hmm... Try to do it again...

17. Callisto Group Title

Since you've made a mistake in the first operation, it's hard to get the right answer :|

18. UsukiDoll Group Title

something is wrong with the y

19. UsukiDoll Group Title

ok let's redo this

20. UsukiDoll Group Title

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21. UsukiDoll Group Title

augmented matrix [a b]

22. UsukiDoll Group Title

|dw:1361067630686:dw| triangles indicate main diagonal

23. UsukiDoll Group Title

so I have to get rid of the 4 and the -3.

24. UsukiDoll Group Title

2row 1 - row 2 --> row2

25. Callisto Group Title

Hmm.. My usual practice is -2R1 + R2 -> R2

26. UnkleRhaukus Group Title

do you mean $R_2\to R_2-2R_1$ @UsukiDoll

27. UsukiDoll Group Title

yes

28. UsukiDoll Group Title

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29. UsukiDoll Group Title

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30. UsukiDoll Group Title

so now... to get rid of the -3... 7row1 -3row2 --->row1

31. Callisto Group Title

Why not do this: -1/7 R2 -> R2

32. UsukiDoll Group Title

achhhhhhhhhhhh

33. UsukiDoll Group Title

I don't wanna deal with fractions

34. Callisto Group Title

But the answers are fractions :P

35. UnkleRhaukus Group Title

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36. UsukiDoll Group Title

arghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh I feel like Rarity Belle now

37. Callisto Group Title

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38. UsukiDoll Group Title

oh wait. sign errors everywhere. Is that why I am getting frustrateD?

39. UsukiDoll Group Title

wait a sec something is wrong already with row 2

40. UsukiDoll Group Title

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41. UsukiDoll Group Title

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42. Callisto Group Title

Relax~~~ |dw:1361068054013:dw|

43. UsukiDoll Group Title

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44. UsukiDoll Group Title

argh there could be so many combinations with this thing!

45. Callisto Group Title

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46. UsukiDoll Group Title

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47. UsukiDoll Group Title

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48. Callisto Group Title

Just stop for a while, if you don't mind?

49. UsukiDoll Group Title

arghhhhhhhhhhhhh doing that got me x = 7

50. Callisto Group Title

This is basically what you do for the first row operation -2R1 + R2 -> R2. I split it into two steps so that you can catch up the the arithmetic easier (I hope..) |dw:1361068290374:dw|

51. UsukiDoll Group Title

big numbers -_-

52. UsukiDoll Group Title

that means to get rid of the 6 I have to do 7r1 - 6r2

53. Callisto Group Title

No?!

54. UsukiDoll Group Title

or -7r1+6r2

55. UsukiDoll Group Title

-.-

56. UsukiDoll Group Title

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57. UsukiDoll Group Title

|dw:1361068472375:dw| main diagonal in triangles

58. UsukiDoll Group Title

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59. UsukiDoll Group Title

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60. Callisto Group Title

Yup..Do you want to deal with big numbers or fractions?

61. UsukiDoll Group Title

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62. UsukiDoll Group Title

I don't want to deal with fractions

63. UsukiDoll Group Title

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64. Callisto Group Title

Yes!!!

65. UsukiDoll Group Title

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66. UsukiDoll Group Title

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67. UsukiDoll Group Title

ok why the heck am I getting different answers despite the fact that I got it into reduced row echleon form. that's just...grrrrrrrrrrrrrrrrrr

68. UsukiDoll Group Title

just earlier I got x = -1 and y = -2

69. Callisto Group Title

Hmm.. Careless mistakes perhaps?!

70. UsukiDoll Group Title

now x = 1/7 y = -18/7

71. UsukiDoll Group Title

what!

72. Callisto Group Title

The one x=1/7; y=-18/7 is right :\

73. UsukiDoll Group Title

-.- is there more than one answer to this? There could be many many things that I could have done here.

74. Callisto Group Title

No.

75. UnkleRhaukus Group Title

x = 1/7 y = -18/7 $$\LARGE\checkmark$$

76. Callisto Group Title

There are only 3 cases for system of linear equations.. 1. No solution 2. Exactly one solution 3. Infinitely many solution.

77. UsukiDoll Group Title

78. UnkleRhaukus Group Title

A quick string of row operations $R_2\to R_2-2R_1\\R_2\to R_2/7\\ R_1\to R_1+3R_2\\R_1\to R_1/2$, if you have gotten a different solution you must have a made a mistake somewhere, it is very easy to make mistakes using Gauss–Jordan elimination .

79. Callisto Group Title

1. No solution with a row that has all zero entries on the left, but non-zero entry on right => system is inconsistent 2. Exactly one solution After elementary row operations, no. of rows = no. of unknowns (/columns) => system is consistent 3. Infinitely many solution. After elementary row operations, no. of rows < no. of unknowns => system is consistent

80. UsukiDoll Group Title

but...yeah I suppose because I have seen some matrices that had a row of zeros on the left but with a nonzero on the right that is an inconsistent system .. How is it possible to make a mistake when it's so hard to spot one? I mean...I could've used different operations on the matrix. The combinations are everywhere.

81. UsukiDoll Group Title

Gauss Jordan is worse than Gaussian

82. UsukiDoll Group Title

ohhhhh what happens if I did Gaussian and then Gauss Jordon

83. UsukiDoll Group Title

because the answers to the Gaussian are supposed to be the same as the Gauss Jordon

84. Callisto Group Title

Gaussian Jordan = Gaussian then Jordan lol!!!

85. UsukiDoll Group Title

but sometimes when I put the matrix into echleon form I can see the steps to making it row reduced

86. UsukiDoll Group Title

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87. Callisto Group Title

Guassian told you to make the left an upper triangular matrix Jordan asked you to further make the left an identity matrix

88. Callisto Group Title

*Gaussian

89. UsukiDoll Group Title

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90. UsukiDoll Group Title

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91. UsukiDoll Group Title

-____________________- this is just Gaussian... WHAT THEEEEE!!!!!!! I see y = -18/7 oh I haven't solved yet oops

92. UsukiDoll Group Title

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93. Callisto Group Title

Just a minute..

94. UsukiDoll Group Title

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95. UsukiDoll Group Title

uighhhhhhhhhhhhhhhh mind blown

96. UsukiDoll Group Title

Gaussian and then Gaussian Jordan yeahhhhh

97. UsukiDoll Group Title

I found the x = 1/7 just doing the Gaussian

98. Callisto Group Title

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99. UsukiDoll Group Title

yeahhhh...now I really should've done Gaussian first and then the Jordan version

100. Callisto Group Title

Gaussian -> Make the left an upper triangular matrix Jordan -> Make the left an identity matrix Gaussian-Jordan => Make it an upper triangular matrix, then further make it an identity matrix. That's what Gaussan-Jordan is! Jordon helps you to get the answer by matching the left and the right That is for the row [1 0 | 1/7], you can tell immediately that x = 1/7 It's just the same as doing Gaussian elimination then back substitution.

101. UsukiDoll Group Title

dang that means I have to redo some practice problems...gawd not again wasting paper here.

102. UsukiDoll Group Title

oh yeah now I got it

103. UsukiDoll Group Title

yup works. I went way too ahead... x.x

104. UsukiDoll Group Title

so now I gotta correct all of these problems and write a proof...nice X___X

105. UsukiDoll Group Title

Callisto do you know how to write proofs? I got a partial first draft and I was wondering if you could critique it?

106. Callisto Group Title

Are you doing high school maths or college maths?

107. UsukiDoll Group Title

college math