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s3a

  • 2 years ago

Basis for the column space of A problem: For #3(a) [ http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf ], how did the solution go from U to R? when c != 3

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  1. s3a
    • 2 years ago
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    It seems c was chosen to be 4 but why?

  2. ingenuus
    • 2 years ago
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    divide the second row by (c-3)

  3. ingenuus
    • 2 years ago
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    subtract row2 from row1

  4. ingenuus
    • 2 years ago
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    and so on..

  5. ingenuus
    • 2 years ago
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    c was not chosen to be 4

  6. s3a
    • 2 years ago
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    I get this: http://i.imgur.com/RIZgXlJ.jpg

  7. s3a
    • 2 years ago
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    with what you said

  8. ingenuus
    • 2 years ago
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    good :)

  9. s3a
    • 2 years ago
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    Wait, I think we're miscommunicating. I meant that as in I did what you said and there are still "c"s floating around.

  10. ingenuus
    • 2 years ago
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    well subtract (-4/(c-3))(row3) from row2 and subtract (2+4/(c-3))(row3) from row1

  11. ingenuus
    • 2 years ago
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    i think you should look again row reduced echelon form

  12. s3a
    • 2 years ago
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    but wouldn't that have the position which currently has the leading ones' with "c"s?

  13. s3a
    • 2 years ago
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    Also, sorry for being slow right now, my brain is being overworked and I can't take a break because I have exams.

  14. ingenuus
    • 2 years ago
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    no it won't

  15. ingenuus
    • 2 years ago
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    look at the picture you uploaded

  16. ingenuus
    • 2 years ago
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    row 3 is 1 1

  17. s3a
    • 2 years ago
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    OH!

  18. ingenuus
    • 2 years ago
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    to get the row reduced echelon form, you will make everything zero above pivots right?

  19. s3a
    • 2 years ago
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    Yes, I see it. :D Let me just confirm, I get the same answer.

  20. ingenuus
    • 2 years ago
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    well since row3 is 1 1 it will remove same things above ok i see you got it

  21. s3a
    • 2 years ago
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    I've confirmed that I got it. :D Thanks a lot.

  22. s3a
    • 2 years ago
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    !

  23. s3a
    • 2 years ago
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    "row 3 is 1 1" is what made me see it instantly.

  24. s3a
    • 2 years ago
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    (Just saying.)

  25. ingenuus
    • 2 years ago
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    good luck on your exam! :)

  26. s3a
    • 2 years ago
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    Thanks. :)

  27. s3a
    • 2 years ago
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    (Also, good luck on yours if you have any.)

  28. s3a
    • 2 years ago
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    Actually, I have another question. Why does it matter what c is equal to if it dissapears thanks to elimination? (Sorry if that's a dumb question.)

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