Results 1 to 4 of 4

Math Help - Similar matrices

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

    Similar matrices

    Show that A and B are similar by finding M so that B=M^{-1}AM.

    A=\left[ \begin{array}{cc} 1 & 0 \\ 1 & 0 \end{array} \right]

    B=\left[ \begin{array}{cc} 1 & 0 \\ 0 & 0 \end{array} \right]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602
    Well, define \displaystyle M = \left[\begin{matrix}a&b\\c&d\end{matrix}\right] so that \displaystyle M^{-1} = \frac{1}{ad - bc}\left[\begin{matrix}\phantom{-}d&-b\\-c&\phantom{-}a\end{matrix}\right].

    What is \displaystyle M^{-1}AM? Set it equal to \displaystyle B and see if you can solve for \displaystyle a,b,c,d.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,441
    Thanks
    1862
    Equivalently, B= M^{-1}AM is the same as MB= AM so set
    \begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}= \begin{bmatrix}1 & 0 \\ 1 & 0\end{bmatrix}\begin{bmatrix}a & b \\ c & d\end{bmatrix}
    and solve for a, b, c, and d.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by HallsofIvy View Post
    Equivalently, B= M^{-1}AM is the same as MB= AM so set
    \begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}= \begin{bmatrix}1 & 0 \\ 1 & 0\end{bmatrix}\begin{bmatrix}a & b \\ c & d\end{bmatrix}
    and solve for a, b, c, and d.
    M=\begin{bmatrix}a & 0 \\ a & d\end{bmatrix}
    Last edited by alexmahone; April 9th 2011 at 09:44 AM. Reason: Stupid mistake
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Are these matrices similar?
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 24th 2011, 01:18 AM
  2. Similar matrices Q
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: July 30th 2011, 04:41 AM
  3. similar matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 26th 2009, 05:26 PM
  4. Similar matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 10th 2008, 06:17 PM
  5. Similar Matrices
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2006, 08:12 PM

/mathhelpforum @mathhelpforum