• Support PF! Buy your school textbooks, materials and every day products Here!

Linear algebra-2x2 RREF matrices

  • Thread starter pyroknife
  • Start date
  • #1
613
3

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
123
0
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
Science Advisor
Homework Helper
26,258
618
What about:

1 a
0 0

where a is nonzero and not 1?
 
  • #4
123
0
Truth [itex]\downarrow[/itex]

What about:

1 a
0 0

where a is nonzero?
 
  • #5
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
Science Advisor
Homework Helper
26,258
618
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
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
Science Advisor
Homework Helper
26,258
618
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!
 

Related Threads for: Linear algebra-2x2 RREF matrices

Replies
10
Views
12K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
983
Replies
5
Views
2K
Top