# Math Help - How many types of 2x2 matrices are there in reduced row-echelon form?

1. ## How many types of 2x2 matrices are there in reduced row-echelon form?

Here is what I have thought through so far:

There are two 2x2 matrices of the same type that are in reduced row echelon form. The first is the zero matrix.

0 0
0 0

The second is the matrix of the form:

1 0
0 1

Is this correct, or am I misunderstanding the question?

Thanks for your help.

2. Originally Posted by centenial

Here is what I have thought through so far:

There are two 2x2 matrices of the same type that are in reduced row echelon form. The first is the zero matrix.

0 0
0 0

The second is the matrix of the form:

1 0
0 1

Is this correct, or am I misunderstanding the question?

Thanks for your help.

$\displaystyle\begin{bmatrix}1&0\\0&0\end{bmatrix}$

3. Thanks! I missed that... and I guess I also missed:

0 1
0 0

Because I think that matrix is in rref. I'm still not 100% sure I'm clear on what the question is asking for. Am I going in the right direction?

4. Originally Posted by centenial
Thanks! I missed that... and I guess I also missed:

0 1
0 0

Because I think that matrix is in rref. I'm still not 100% sure I'm clear on what the question is asking for. Am I going in the right direction?
I just checked the definition of rref. Every pivot position needs to be a one. Therefore, the answer is 1 or 2. I am not sure if you can include the 0 matrix.

5. In that case, would there be no pivots?

6. By Harvard's definition, we have

$\displaystyle\begin{bmatrix}1&0\\0&1\end{bmatrix}, \ \begin{bmatrix}1&0\\0&0\end{bmatrix}, \ \begin{bmatrix}0&0\\0&0\end{bmatrix}, \begin{bmatrix}0&1\\0&0\end{bmatrix}$