Results 1 to 6 of 6

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

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    57

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

    I'm a little confused about this question:



    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by centenial View Post
    I'm a little confused about this question:



    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.
    What about

    \displaystyle\begin{bmatrix}1&0\\0&0\end{bmatrix}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    57
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by centenial View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    5
    Awards
    2
    In that case, would there be no pivots?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    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}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 4th 2011, 04:06 AM
  2. Help with reduced row echelon form/solving system
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 23rd 2009, 07:35 AM
  3. row reduced echelon form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 11th 2009, 08:46 PM
  4. [Reduced] Column Echelon Form
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 23rd 2008, 08:45 PM
  5. Replies: 7
    Last Post: December 24th 2007, 10:17 PM

Search Tags


/mathhelpforum @mathhelpforum