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Linear algebra-2x2 RREF matrices

  1. Aug 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Give examples to describe all 2 × 2 reduced row
    echelon matrices


    3. The attempt at a solution

    Not sure how to type matrices on here.
    I came up with 5 different ones:

    0 0
    0 0

    1 0
    0 1

    0 1
    0 0

    1 0
    0 0

    1 1
    0 0
    Are there any I'm missing? i can't think of any more than these 5 matrices. Also the problem asks me to give examples to describe all 2x2 RREF matrices. How do I "describe" it or is providing all 5 matrices sufficient>?
     
  2. jcsd
  3. Aug 28, 2012 #2
    I would consider "describing" all 2x2 RREF matrices as simply listing them, so I would think that you are done.

    Could you quote the problem exactly?
     
  4. Aug 28, 2012 #3

    Dick

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    What about:

    1 a
    0 0

    where a is nonzero and not 1?
     
  5. Aug 28, 2012 #4
    Truth [itex]\downarrow[/itex]

     
  6. Aug 28, 2012 #5
    I copy and pasted the instructions. I think all I need to do is list them, but I'll check with my prof tomorrow.
    !!! DAng it. Would've never thought of that one. Using that matrix means there are infinite matrices of that form. Or I can classify it as one form with a variable.
     
  7. Aug 28, 2012 #6

    Dick

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    Sure, list it like that. Then you can drop:

    1 1
    0 0

    It's a special case.
     
  8. Aug 28, 2012 #7
    Thanks a bunch for the help guys.

    What do you mean by special case?

    Or could I also drop
    1 0
    0 0
    and define a is any number?
     
  9. Aug 28, 2012 #8

    Dick

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    Good idea!
     
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