Results 1 to 3 of 3

Math Help - How to find inverse matrix of a 3*3 or of having order > 3 in a easy way

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    2

    Talking How to find inverse matrix of a 3*3 or of having order > 3 in a easy way

    I know finding inverse of a matrix in 3 ways 1) if 2*2 1/(ad-bc)[d -b] [-c a] 2) if order is >3 by elementary row operations with identity matrix [ -1 2 -3 | 1 0 0 ] [ 2 1 0 | 0 1 0 ] [ 4 -2 5 | 0 0 1 ] like dis on reducing into In ; B 3) through eigen value process sir all of dese processes are taking bulk of time in xams. I request you to tell me if u r known with any other easiest way
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Swlabr's Avatar
    Joined
    May 2009
    Posts
    1,176
    Quote Originally Posted by achasiri View Post
    I know finding inverse of a matrix in 3 ways 1) if 2*2 1/(ad-bc)[d -b] [-c a] 2) if order is >3 by elementary row operations with identity matrix [ -1 2 -3 | 1 0 0 ] [ 2 1 0 | 0 1 0 ] [ 4 -2 5 | 0 0 1 ] like dis on reducing into In ; B 3) through eigen value process sir all of dese processes are taking bulk of time in xams. I request you to tell me if u r known with any other easiest way
    Write out your post properly, pressing the `return' key every once in a while and spelling `these' correctly, and then I will tell you my thoughts on the matter (your post is pretty much illegible the way it is).

    Also, to get the matrix to be displayed correctly, use LaTeX.

    Finally, what do you mean by `order 3'? Do you mean a 3x3 matrix, or a matrix A such that A^3=Id?
    Last edited by Swlabr; January 25th 2011 at 09:15 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,400
    Thanks
    1848
    Frankly, I believe that row-reduction is the easiest way to find the inverse matrix, even for 3 by 3 and 2 by 2 matrices. However, you can also use the fact that the inverse of the matrix
    A= \begin{bmatrix}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{13} & a_{23} & a_{33}\end{bmatrix}
    is given by
    A^{-1}= \frac{1}{det(A)}\begin{bmatrix}b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{13} & b_{23} & b_{33}\end{bmatrix}
    where b_{ij} is the "minor" of a_{ji} (note the reversal of i and j). The minor is the determinant of the matrix with the row and column a_{ji} is in removed, multiplied by (-1)^{i+j}. This, in fact, will work for any n by n matrix but probably is easier than row-reduction for 2 by 2 and some 3 by 3 matrices.

    As a simple 2 by 2 example, if
    A= \begin{bmatrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{bmatrix}
    then the determinant is a_{11}a_{22}- a_{12}a_{21}, the minor of a_{11} is just a_{22}, the minor of a_{12} is -a_{21}, the minor of a_{21} is -a_{12}, and the minor of a_{22} is a_{11}. Remembering the reversal of "i" and "j", the inverse matrix is
    A^{-1}= \frac{1}{a_{11}a_{22}- a_{12}a_{21}}\begin{bmatrix}a_{22} & -a_{12} \\ -a_{21} & a_{11}\end{bmatrix}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the inverse of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 29th 2009, 01:18 AM
  2. how can i find the inverse of matrix?
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: June 2nd 2009, 12:54 PM
  3. Find the inverse of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 17th 2009, 11:19 AM
  4. Replies: 1
    Last Post: February 10th 2009, 02:54 PM
  5. How to find inverse of matrix?
    Posted in the Calculators Forum
    Replies: 4
    Last Post: October 26th 2008, 10:01 AM

Search Tags


/mathhelpforum @mathhelpforum