Results 1 to 5 of 5

Math Help - Inverse of a matrix

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    19

    Inverse of a matrix

    I am trying to do an inverse of the following matrix but somehow I can't work it out.

    The given matrix is this:
    Code:
    1 1 0
    1 1 1
    2 1 1
    I added the I matrix to that :
    Code:
    1 1 0 | 1 0 0 
    1 1 1 | 0 1 0
    2 1 1 | 0 0 1
    and started to reducing to upper triangular form:

    I tried
    Row2 = Row2 - Row1
    Row3 = Row3 - 2Row1

    but this was the result

    Code:
    1 1 0 | 1 0 0
    0 0 1 | -1 1 0
    0 -1 1| -2 0 1
    and I got stuck there.

    Isit perhaps because I am doing something wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Inverse of a matrix

    Quote Originally Posted by terence View Post
    but this was the result

    Code:
    1 1 0 | 1 0 0
    0 0 1 | -1 1 0
    0 -1 1| -2 0 1
    and I got stuck there.

    Isit perhaps because I am doing something wrong?
    You now need to exchange rows 2 and 3.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    Posts
    19

    Re: Inverse of a matrix

    You now need to exchange rows 2 and 3.
    Well, That's what I actually thought because it becomes perfect then, but this is just a matrix not a system of equations.
    eg
    Code:
    1 2 3 | 5
    4 5 6 | 7
    7 8 9 | 8
    (just invented for an example)

    I think that is possible in only system of equations or am i wrong?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,814
    Thanks
    703

    Re: Inverse of a matrix

    Hello, terence!

    alexmahone's suggestion is excellent!
    Or you can solve it head-on.


    \text{Find the inverse of }\:A \;=\;\begin{vmatrix}1&1&0 \\ 1&1&1 \\ 2&1&1\end{vmatrix}

    \text{We have: }\:\begin{array}{|ccc|ccc|}1&1&0&1&0&0  \\ 1&1&1&0&1&0 \\ 2&1&1&0&0&1 \end{array}


    \begin{array}{c}\\ R_2 - R_1 \\ R_3 - 2R_1 \end{array}\begin{array}{|ccc|ccc|} 1&1&0 & 1&0&0 \\ 0&0&1 & \text{-}1&1&0 \\ 0&\text{-}1&1 & \text{-}2&0&1 \end{array}


    \begin{array}{c} R_1+R_3 \\ R_2-R_3 \\ \ \end{array}\begin{array}{|ccc|ccc|} 1&0&1 & \text{-}1&0&1 \\ 0&1&0 & 1&1&\text{-}1 \\ 0&\text{-}1 &1 & \text{-}2&0&1 \end{array}


    \begin{array}{c} \\ \\ R_3 + R_2 \end{array}\begin{array}{|ccc|ccc|} 1&0&1 & \text{-}1&0&1 \\ 0&1&0 & 1&1&\text{-}1 \\ 0&0&1 & \text{-}1&1&0 \end{array}


    \begin{array}{c}R-R_3 \\ \\ \\ \end{array} \begin{array}{|ccc|ccc|} 1&0&0 & 0&\text{-}1&1 \\ 0&1&0 & 1&1&\text{-}1 \\ 0&0&1 & \text{-}1&1&0 \end{array}


    Therefore: . A^{-1} \;=\;\begin{array}{|ccc|} 0&\text{-}1 & 1 \\ 1 & 1 & \text{-}1 \\ \text{-}1 & 1 & 0 \end{array}

    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,004
    Thanks
    1660

    Re: Inverse of a matrix

    I am confused as to what you are asking. There are three types of "row operation": multiply a single row by a number, add a multiple of one row to another (the multiple can be negative), and interchange two rows. You can use them to solve a system of equations by writing the equations as matrices but that is not the only use of row operations. They can be used to find inverse matrices, as you do here, or to find the determinant of a matrix.

    What you give would be written as
    \begin{bmatrix}1 & 2 & 3 & 5 \\ 4 & 5 & 6 & 7\\ 7 & 8 & 9 & 8\end{bmatrix}
    (I removed the vertical line because that is not part of a matrix- that would be used to identify the right hand side of a system of equations, which you say you are not talking about.)

    Yes, you can apply all row operations to that matrix- but to what purpose? What do you want to do with this matrix?
    Last edited by HallsofIvy; November 18th 2011 at 10:46 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Finding the inverse of a matrix using it's elementary matrix?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 7th 2011, 06:08 PM
  2. [SOLVED] Derivative of a matrix inverse and matrix determinant
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 24th 2011, 08:18 AM
  3. 3x3 matrix inverse
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: June 1st 2010, 05:01 AM
  4. Replies: 3
    Last Post: March 1st 2010, 06:22 AM
  5. the inverse of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 2nd 2009, 10:26 AM

Search Tags


/mathhelpforum @mathhelpforum