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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

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  1. UsukiDoll Group Title
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    |dw:1361067093589:dw|

    • one year ago
  2. UsukiDoll Group Title
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    |dw:1361067118822:dw|

    • one year ago
  3. UsukiDoll Group Title
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    ugh I missed that one on my paper! that subtraction because -16-(-2) is - 14

    • one year ago
  4. UsukiDoll Group Title
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    anyway|dw:1361067211535:dw|

    • one year ago
  5. UsukiDoll Group Title
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    |dw:1361067247174:dw|

    • one year ago
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    |dw:1361067302376:dw|

    • one year ago
  7. Callisto Group Title
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    |dw:1361067336310:dw|

    • one year ago
  8. UsukiDoll Group Title
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    |dw:1361067340708:dw|

    • one year ago
  9. Callisto Group Title
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    |dw:1361067371987:dw|

    • one year ago
  10. UsukiDoll Group Title
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    I'm using elementary row operations.

    • one year ago
  11. UsukiDoll Group Title
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    oh crud

    • one year ago
  12. UsukiDoll Group Title
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    spotted anotehr error. not my day today

    • one year ago
  13. UsukiDoll Group Title
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    |dw:1361067436003:dw|

    • one year ago
  14. UsukiDoll Group Title
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    arghhh...

    • one year ago
  15. UsukiDoll Group Title
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    ok really...I put this in reduced row echleon form. got my solution, but geez doesn't even equal back into the equation

    • one year ago
  16. Callisto Group Title
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    Hmm... Try to do it again...

    • one year ago
  17. Callisto Group Title
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    Since you've made a mistake in the first operation, it's hard to get the right answer :|

    • one year ago
  18. UsukiDoll Group Title
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    something is wrong with the y

    • one year ago
  19. UsukiDoll Group Title
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    ok let's redo this

    • one year ago
  20. UsukiDoll Group Title
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    |dw:1361067604121:dw|

    • one year ago
  21. UsukiDoll Group Title
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    augmented matrix [a b]

    • one year ago
  22. UsukiDoll Group Title
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    |dw:1361067630686:dw| triangles indicate main diagonal

    • one year ago
  23. UsukiDoll Group Title
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    so I have to get rid of the 4 and the -3.

    • one year ago
  24. UsukiDoll Group Title
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    2row 1 - row 2 --> row2

    • one year ago
  25. Callisto Group Title
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    Hmm.. My usual practice is -2R1 + R2 -> R2

    • one year ago
  26. UnkleRhaukus Group Title
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    do you mean \[R_2\to R_2-2R_1\] @UsukiDoll

    • one year ago
  27. UsukiDoll Group Title
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    yes

    • one year ago
  28. UsukiDoll Group Title
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    |dw:1361067762579:dw|

    • one year ago
  29. UsukiDoll Group Title
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    |dw:1361067803078:dw|

    • one year ago
  30. UsukiDoll Group Title
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    so now... to get rid of the -3... 7row1 -3row2 --->row1

    • one year ago
  31. Callisto Group Title
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    Why not do this: -1/7 R2 -> R2

    • one year ago
  32. UsukiDoll Group Title
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    achhhhhhhhhhhh

    • one year ago
  33. UsukiDoll Group Title
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    I don't wanna deal with fractions

    • one year ago
  34. Callisto Group Title
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    But the answers are fractions :P

    • one year ago
  35. UnkleRhaukus Group Title
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    |dw:1361067930957:dw|

    • one year ago
  36. UsukiDoll Group Title
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    arghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh I feel like Rarity Belle now

    • one year ago
  37. Callisto Group Title
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    |dw:1361067978329:dw|

    • one year ago
  38. UsukiDoll Group Title
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    oh wait. sign errors everywhere. Is that why I am getting frustrateD?

    • one year ago
  39. UsukiDoll Group Title
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    wait a sec something is wrong already with row 2

    • one year ago
  40. UsukiDoll Group Title
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    |dw:1361068119755:dw|

    • one year ago
  41. UsukiDoll Group Title
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    |dw:1361068152547:dw|

    • one year ago
  42. Callisto Group Title
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    Relax~~~ |dw:1361068054013:dw|

    • one year ago
  43. UsukiDoll Group Title
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    |dw:1361068165204:dw|

    • one year ago
  44. UsukiDoll Group Title
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    argh there could be so many combinations with this thing!

    • one year ago
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    |dw:1361068179917:dw|

    • one year ago
  46. UsukiDoll Group Title
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    |dw:1361068217096:dw|

    • one year ago
  47. UsukiDoll Group Title
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    |dw:1361068228254:dw|

    • one year ago
  48. Callisto Group Title
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    Just stop for a while, if you don't mind?

    • one year ago
  49. UsukiDoll Group Title
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    arghhhhhhhhhhhhh doing that got me x = 7

    • one year ago
  50. Callisto Group Title
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    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|

    • one year ago
  51. UsukiDoll Group Title
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    big numbers -_-

    • one year ago
  52. UsukiDoll Group Title
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    that means to get rid of the 6 I have to do 7r1 - 6r2

    • one year ago
  53. Callisto Group Title
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    No?!

    • one year ago
  54. UsukiDoll Group Title
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    or -7r1+6r2

    • one year ago
  55. UsukiDoll Group Title
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    -.-

    • one year ago
  56. UsukiDoll Group Title
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    |dw:1361068464895:dw|

    • one year ago
  57. UsukiDoll Group Title
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    |dw:1361068472375:dw| main diagonal in triangles

    • one year ago
  58. UsukiDoll Group Title
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    |dw:1361068495592:dw|

    • one year ago
  59. UsukiDoll Group Title
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    |dw:1361068548208:dw|

    • one year ago
  60. Callisto Group Title
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    Yup..Do you want to deal with big numbers or fractions?

    • one year ago
  61. UsukiDoll Group Title
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    |dw:1361068571208:dw|

    • one year ago
  62. UsukiDoll Group Title
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    I don't want to deal with fractions

    • one year ago
  63. UsukiDoll Group Title
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    |dw:1361068639980:dw|

    • one year ago
  64. Callisto Group Title
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    Yes!!!

    • one year ago
  65. UsukiDoll Group Title
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    |dw:1361068650303:dw|

    • one year ago
  66. UsukiDoll Group Title
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    |dw:1361068693152:dw|

    • one year ago
  67. UsukiDoll Group Title
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    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

    • one year ago
  68. UsukiDoll Group Title
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    just earlier I got x = -1 and y = -2

    • one year ago
  69. Callisto Group Title
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    Hmm.. Careless mistakes perhaps?!

    • one year ago
  70. UsukiDoll Group Title
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    now x = 1/7 y = -18/7

    • one year ago
  71. UsukiDoll Group Title
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    what!

    • one year ago
  72. Callisto Group Title
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    The one x=1/7; y=-18/7 is right :\

    • one year ago
  73. UsukiDoll Group Title
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    -.- is there more than one answer to this? There could be many many things that I could have done here.

    • one year ago
  74. Callisto Group Title
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    No.

    • one year ago
  75. UnkleRhaukus Group Title
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    x = 1/7 y = -18/7 \(\LARGE\checkmark\)

    • one year ago
  76. Callisto Group Title
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    There are only 3 cases for system of linear equations.. 1. No solution 2. Exactly one solution 3. Infinitely many solution.

    • one year ago
  77. UsukiDoll Group Title
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    I had a truckload

    • one year ago
  78. UnkleRhaukus Group Title
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    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 .

    • one year ago
  79. Callisto Group Title
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    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

    • one year ago
  80. UsukiDoll Group Title
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    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.

    • one year ago
  81. UsukiDoll Group Title
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    Gauss Jordan is worse than Gaussian

    • one year ago
  82. UsukiDoll Group Title
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    ohhhhh what happens if I did Gaussian and then Gauss Jordon

    • one year ago
  83. UsukiDoll Group Title
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    because the answers to the Gaussian are supposed to be the same as the Gauss Jordon

    • one year ago
  84. Callisto Group Title
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    Gaussian Jordan = Gaussian then Jordan lol!!!

    • one year ago
  85. UsukiDoll Group Title
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    but sometimes when I put the matrix into echleon form I can see the steps to making it row reduced

    • one year ago
  86. UsukiDoll Group Title
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    |dw:1361069849783:dw|

    • one year ago
  87. Callisto Group Title
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    Guassian told you to make the left an upper triangular matrix Jordan asked you to further make the left an identity matrix

    • one year ago
  88. Callisto Group Title
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    *Gaussian

    • one year ago
  89. UsukiDoll Group Title
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    |dw:1361069869054:dw|

    • one year ago
  90. UsukiDoll Group Title
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    |dw:1361069916982:dw|

    • one year ago
  91. UsukiDoll Group Title
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    -____________________- this is just Gaussian... WHAT THEEEEE!!!!!!! I see y = -18/7 oh I haven't solved yet oops

    • one year ago
  92. UsukiDoll Group Title
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    |dw:1361070002077:dw|

    • one year ago
  93. Callisto Group Title
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    Just a minute..

    • one year ago
  94. UsukiDoll Group Title
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    |dw:1361070023727:dw|

    • one year ago
  95. UsukiDoll Group Title
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    uighhhhhhhhhhhhhhhh mind blown

    • one year ago
  96. UsukiDoll Group Title
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    Gaussian and then Gaussian Jordan yeahhhhh

    • one year ago
  97. UsukiDoll Group Title
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    I found the x = 1/7 just doing the Gaussian

    • one year ago
  98. Callisto Group Title
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    |dw:1361070037568:dw|

    • one year ago
  99. UsukiDoll Group Title
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    yeahhhh...now I really should've done Gaussian first and then the Jordan version

    • one year ago
  100. Callisto Group Title
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    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.

    • one year ago
  101. UsukiDoll Group Title
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    dang that means I have to redo some practice problems...gawd not again wasting paper here.

    • one year ago
  102. UsukiDoll Group Title
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    oh yeah now I got it

    • one year ago
  103. UsukiDoll Group Title
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    yup works. I went way too ahead... x.x

    • one year ago
  104. UsukiDoll Group Title