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aspenfields

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

  • one year ago
  • one year ago

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  1. beketso
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    are you familiar with matrices

    • one year ago
  2. aspenfields
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    kinda

    • one year ago
  3. beketso
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    well you can use the gaussian elimination

    • one year ago
  4. aspenfields
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    ok

    • one year ago
  5. beketso
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    meaning you use the elementary row operations

    • one year ago
  6. aspenfields
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    yea

    • one year ago
  7. beketso
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    2 4 3 | 6 3 5 6 | 3 2 3 4 | 8 subtract row 1 from row 3 and tell me what u get

    • one year ago
  8. aspenfields
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    ok one sec

    • one year ago
  9. aspenfields
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    0 -1 1 |2 is that right?

    • one year ago
  10. beketso
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    yeah.now divide row 1 by 2

    • one year ago
  11. aspenfields
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    ok the answer i have above isnt row one is it or is row one in the problem still?

    • one year ago
  12. beketso
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    no.it is still row 3.row one is ur original problem 2 4 3 | 6

    • one year ago
  13. aspenfields
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    ok

    • one year ago
  14. aspenfields
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    2/3 4/5 1/2 |2 right?

    • one year ago
  15. beketso
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    it is actually 1 2 3/2 | 3 get it?

    • one year ago
  16. aspenfields
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    how?

    • one year ago
  17. beketso
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    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

    • one year ago
  18. aspenfields
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    ohh! u divid by two not thr 2nd row :/lol now i got that ok

    • one year ago
  19. beketso
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    then your rows are now like this 1 2 3/2 | 3 3 5 6 | 3 0 -1 1 | 2

    • one year ago
  20. aspenfields
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    yea

    • one year ago
  21. beketso
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    sorry. multipy row 1 by 3 the subtract it from row 2 the u have a reduced row 2

    • one year ago
  22. aspenfields
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    ok? one sec

    • one year ago
  23. aspenfields
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    when i subtract which number should be on top?

    • one year ago
  24. beketso
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    1 2 3/2 | 3 _ _ _ | _ 0 -1 1 | 2 the only r0w that changes is row 2

    • one year ago
  25. aspenfields
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    yea,ok i get that so row to is now 3 8 9/2 |-3

    • one year ago
  26. beketso
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    3-(3X3) = 0 That is how u do it.

    • one year ago
  27. aspenfields
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    what?

    • one year ago
  28. beketso
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    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

    • one year ago
  29. beketso
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    then u get 1 2 3/2 | 3 0 -1 3/2 | -6 0 -1 1 | 2

    • one year ago
  30. aspenfields
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    ohh

    • one year ago
  31. aspenfields
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    ok then from there what do i do next ?

    • one year ago
  32. beketso
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    multiply row 2 by -1

    • one year ago
  33. aspenfields
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    ok

    • one year ago
  34. aspenfields
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    0 1 -3/2 |6

    • one year ago
  35. beketso
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    exactly

    • one year ago
  36. aspenfields
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    ok is this the answer or is the more?

    • one year ago
  37. beketso
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    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.

    • one year ago
  38. aspenfields
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    why?

    • one year ago
  39. beketso
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    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

    • one year ago
  40. aspenfields
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    ok

    • one year ago
  41. beketso
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    sorry u jst eliminated -1 from row 3

    • one year ago
  42. beketso
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    then now we eliminate 2 from row 1

    • one year ago
  43. aspenfields
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    i figured u ment that

    • one year ago
  44. aspenfields
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    :)

    • one year ago
  45. beketso
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    do this row1-2(row2)

    • one year ago
  46. beketso
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    then u get 1 0 9/2 |-9 0 1 -3/2 | 6 0 0 1/2 |-4

    • one year ago
  47. beketso
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    getting this?

    • one year ago
  48. aspenfields
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    yea

    • one year ago
  49. beketso
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    basically u want to get to a point were u have 1 0 0 | ? 0 1 0 | ? 0 0 1 | ?

    • one year ago
  50. beketso
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    now divide row 3 by 1/2 (half)

    • one year ago
  51. aspenfields
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    ohh ok

    • one year ago
  52. aspenfields
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    1 |-2

    • one year ago
  53. beketso
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    what is 4 divided by half

    • one year ago
  54. aspenfields
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    oh 8

    • one year ago
  55. beketso
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    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?

    • one year ago
  56. aspenfields
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    2/9?

    • one year ago
  57. beketso
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    what about 2/9?

    • one year ago
  58. aspenfields
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    u mulitply?

    • one year ago
  59. beketso
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    remember you want it to be 0

    • one year ago
  60. aspenfields
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    on then subtract 9/2?

    • one year ago
  61. beketso
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    exactly

    • one year ago
  62. aspenfields
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    ok :)

    • one year ago
  63. aspenfields
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    what bout the numbers on the end?

    • one year ago
  64. beketso
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    so mentally multiply row 3 by 9/2

    • one year ago
  65. beketso
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    and then subtract it from row 1

    • one year ago
  66. beketso
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    what do u get for row1?

    • one year ago
  67. aspenfields
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    1 0 0 |1?

    • one year ago
  68. beketso
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    actually 1 0 0 |27

    • one year ago
  69. aspenfields
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    oh

    • one year ago
  70. beketso
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    now u got 1 0 0 | 27 0 1 -3/2 |6 0 0 1 |-8

    • one year ago
  71. beketso
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    u must now eliminate -3/2.how do u think u do that?

    • one year ago
  72. aspenfields
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    yes

    • one year ago
  73. beketso
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    how do you think u can do it?

    • one year ago
  74. aspenfields
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    plus 3/2

    • one year ago
  75. beketso
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    sure.which row can u use to eliminate it?

    • one year ago
  76. aspenfields
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    3

    • one year ago
  77. beketso
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    good.how do u do that?

    • one year ago
  78. aspenfields
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    idk

    • one year ago
  79. beketso
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    multiply row3 by 3/2 and add it to row2

    • one year ago
  80. aspenfields
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    ok

    • one year ago
  81. beketso
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    that way 1 becomes 3/2 and you can add that to row 2.the -3/2 + 3/2 = 0 which eliminates 3/2

    • one year ago
  82. aspenfields
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    yea

    • one year ago
  83. beketso
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    then u have 1 0 0 |27 0 1 0 |-6 0 0 1 |-8 what is ur x,y and z?

    • one year ago
  84. aspenfields
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    27,-6,-8?

    • one year ago
  85. beketso
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    yes

    • one year ago
  86. aspenfields
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    ok

    • one year ago
  87. beketso
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    but i think i made a mistake with the numbers somewhere

    • one year ago
  88. beketso
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    should i paste the whole solution or can u figure out the mistake?

    • one year ago
  89. aspenfields
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    i can figure it out now

    • one year ago
  90. beketso
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    ok.sure

    • one year ago
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