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jcd2012 Group Title

Linear Algebra: Find (if possible) values a, b, and c such that the system of linear equations has: a) no solution b) exactly one solution c) infinitely many solutions 2x - y + z = a x +y +2z = b 3y + 3z = c

  • one year ago
  • one year ago

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  1. jcd2012 Group Title
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    |dw:1348174076973:dw|

    • one year ago
  2. inkyvoyd Group Title
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    Try turning that into eschelon form.

    • one year ago
  3. TuringTest Group Title
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    I am thinking a bit differently...

    • one year ago
  4. inkyvoyd Group Title
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    Yeah, I skimmed through a textbok about 30 mins ago, I'm haven't exactly even taken this ;). I know a solution though, it's probably not the most efficient way...

    • one year ago
  5. TuringTest Group Title
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    I'm not sure myself either...

    • one year ago
  6. TuringTest Group Title
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    For any \(n\times n\) matrix \(A\) the system\[A\vec x=\vec b\]has exactly one solution for each \(n\times1\) matrix \(\vec b\) if and only if \(\det A\neq0\)

    • one year ago
  7. TuringTest Group Title
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    so what does a,b, and c have to do with the answer to your question I'm not even sure, the answer seems to be dependent on the matrix \(A\)....

    • one year ago
  8. jcd2012 Group Title
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    a, b, and c are any real number such that each condition is met

    • one year ago
  9. TuringTest Group Title
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    right, any matrix \(\vec b\)

    • one year ago
  10. jcd2012 Group Title
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    |dw:1348174993843:dw|

    • one year ago
  11. jcd2012 Group Title
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    now, do I look for conditions in which the three cases can be met?

    • one year ago
  12. TuringTest Group Title
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    if this is always true then there are infinite solutions, so that would suggest that a=-3, c=3, and b is whatever (easy to figure out) how to test the other two conditions I'm not so sure

    • one year ago
  13. jcd2012 Group Title
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    I'll start with that then. these kinds of questions happen to be the even numbered problems. thanks

    • one year ago
  14. TuringTest Group Title
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    sure, wish I could help more

    • one year ago
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