Linear algebra-2x2 RREF matrices

  • Thread starter pyroknife
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  • #1
pyroknife
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Homework Statement


Give examples to describe all 2 × 2 reduced row
echelon matrices


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>?
 

Answers and Replies

  • #2
christoff
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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?
 
  • #3
Dick
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What about:

1 a
0 0

where a is nonzero and not 1?
 
  • #4
christoff
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0
Truth [itex]\downarrow[/itex]

What about:

1 a
0 0

where a is nonzero?
 
  • #5
pyroknife
613
3
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?
I copy and pasted the instructions. I think all I need to do is list them, but I'll check with my prof tomorrow.
What about:

1 a
0 0

where a is nonzero and not 1?

! 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.
 
  • #6
Dick
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Hey, 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.

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

1 1
0 0

It's a special case.
 
  • #7
pyroknife
613
3
Sure, list it like that. Then you can drop:

1 1
0 0

It's a special case.
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?
 
  • #8
Dick
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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?

Good idea!
 

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