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octoberchick1011

  • 2 years ago

Solve the system using an augmented matrix. Please show all your steps! Thanks! (: -x -3y = -17 2x -6y = -26

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  1. amistre64
    • 2 years ago
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    can you set up the matrix?

  2. octoberchick1011
    • 2 years ago
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    Yes: -1 -3 | -17 2 -6 | 26

  3. jim_thompson5910
    • 2 years ago
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    Your next step is to make the upper left corner equal to 1. How do we do this?

  4. octoberchick1011
    • 2 years ago
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    Umm.. I'm not entirely sure - I'm not very good at these types of problems. I think we would multiply by -3 right...?

  5. jim_thompson5910
    • 2 years ago
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    What do we multiply -1 by to get 1 ?

  6. jim_thompson5910
    • 2 years ago
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    -1 times ??? = 1

  7. octoberchick1011
    • 2 years ago
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    -1.

  8. jim_thompson5910
    • 2 years ago
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    so do this across the entire first row....ie multiply EVERY number in row 1 by -1

  9. jim_thompson5910
    • 2 years ago
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    -1 -3 | -17 2 -6 | 26 1 3 | 17 -1*R1 2 -6 | 26

  10. jim_thompson5910
    • 2 years ago
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    The notation -1*R1 means "-1 times Row 1"

  11. octoberchick1011
    • 2 years ago
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    Okay so it would be: 1 3 | 17 right?

  12. jim_thompson5910
    • 2 years ago
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    yes it would be

  13. jim_thompson5910
    • 2 years ago
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    The upper left corner is a 1. This is known as the pivot (for the first column). Everything thing else must be a zero in order to obtain the solutions for x and y. So how to we turn that 2 (below the pivot of 1) into a 0 ?

  14. jim_thompson5910
    • 2 years ago
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    oh sry, i made a typo the second row should be 2 -6 | -26 instead of 2 -6 | 26

  15. octoberchick1011
    • 2 years ago
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    You would make the 2 a zero my by multiplying it by 0..? I think..

  16. jim_thompson5910
    • 2 years ago
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    well if you did that, everything in row 2 would become 0

  17. jim_thompson5910
    • 2 years ago
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    then you'd get 0x + 0y = 0...which is completely useless now

  18. octoberchick1011
    • 2 years ago
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    Oh. That's true..

  19. jim_thompson5910
    • 2 years ago
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    Instead, you can add/subtract multiples of row 1 to row 2

  20. octoberchick1011
    • 2 years ago
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    So does that mean we would subtract 2 from row 2?

  21. jim_thompson5910
    • 2 years ago
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    Notice in the first column we have 1 2

  22. jim_thompson5910
    • 2 years ago
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    If we subtract row 1 from row 2, we get 2 - 1 = 1 But that's not zero However, if we subtract row 1 (twice) from row 2, we get 2 - 1 - 1 = 0

  23. octoberchick1011
    • 2 years ago
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    Okay. So does that mean that row 2 looks like this now: 0 -6 | -26

  24. jim_thompson5910
    • 2 years ago
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    not quite

  25. jim_thompson5910
    • 2 years ago
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    -6 - 2*(-3) = -12 so the 2nd element in row 2 is -12

  26. octoberchick1011
    • 2 years ago
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    Ugh, I'm so confused - lol, these kinds of probles frustrate me! :P

  27. jim_thompson5910
    • 2 years ago
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    -26 - 2*17 = -60

  28. jim_thompson5910
    • 2 years ago
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    so the 3rd element in row 2 is -60

  29. jim_thompson5910
    • 2 years ago
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    after this, you should have 1 3 | 17 0 -12 | -60

  30. jim_thompson5910
    • 2 years ago
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    what's next?

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