Linear algebra-2x2 RREF matrices

[pyroknife]

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>?

 

[christoff]

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?

 

[Dick]

What about:

1 a
0 0

where a is nonzero and not 1?

 

[christoff]

Truth $\downarrow$

What about:

1 a
0 0

where a is nonzero?

 

[pyroknife]

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.

 

[Dick]

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.

 

[pyroknife]

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?

 

[Dick]

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!