Results 1 to 2 of 2

Math Help - another matrix problem :( sorry

  1. #1
    Member
    Joined
    Apr 2009
    Posts
    108

    another matrix problem :( sorry

    hey guys- these type of questions I dont even know where to begin..

    Suppose a 3 x 3 matrix A can be transofrmed into a 3 x 3 matrix B by the following row operations;

    R2 = R2 - 2R1 , R2 <--> (interchange) R3 and R3 = 1/3 R3

    and that E F and G are the corresponding elementary matrices


    a) write down the matrices E F G and express B in terms of A E F G ??
    B) if det(a) =/= 0 then find det(b)/det(a)

    What does all that mean- I didn't understand a single word what that question or even the information was telling me....

    can some one explain it to me and also do the working out thanks


    I dont understand the question nor the information....

    First I started off like this


    A = ( a b c )
    ( d e f )
    ( g h i )

    I applied all those row operations and then i completly lost it

    Can someone explain to what is elementry matrix ? I tried wikipedia but still coudn't understand it and also what exactly does the question even mean....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Khonics89 View Post
    hey guys- these type of questions I dont even know where to begin..

    Suppose a 3 x 3 matrix A can be transofrmed into a 3 x 3 matrix B by the following row operations;

    R2 = R2 - 2R1 , R2 <--> (interchange) R3 and R3 = 1/3 R3

    and that E F and G are the corresponding elementary matrices


    a) write down the matrices E F G and express B in terms of A E F G ??
    B) if det(a) =/= 0 then find det(b)/det(a)

    What does all that mean- I didn't understand a single word what that question or even the information was telling me....

    can some one explain it to me and also do the working out thanks


    I dont understand the question nor the information....

    First I started off like this


    A = ( a b c )
    ( d e f )
    ( g h i )

    I applied all those row operations and then i completly lost it

    Can someone explain to what is elementry matrix ? I tried wikipedia but still coudn't understand it and also what exactly does the question even mean....
    In a nut shell what they are trying to show is that elementry row operations can be represented as matrix multiplication.

    Example take the identity matrix

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

    If we multiply row 1 by -2 and add it to row 2 we get

    E_1=\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}

    E_2=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0& 1 \\ 0 & 1 & 0\end{bmatrix}


    E_3=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & \frac{1}{3}\end{bmatrix}

    Now for example consider the generic matrix

    \begin{bmatrix} a & b & c \\ d & e & f \\ h& i & j\end{bmatrix}

    If I multiply row 1 by -2 and add it to row 2 I get

    A=\begin{bmatrix} a & b & c \\ d-2a & e-2b & f-2c \\ h& i & j\end{bmatrix}

    Now try it by matrix multiplication(have fun)

    B=\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix} \begin{bmatrix} a & b & c \\ d & e & f \\ h& i & j\end{bmatrix}

    If you do this you will get the same thing.... so in matrix format

    B=E_1A

    I hope this helps get you started
    Last edited by TheEmptySet; May 22nd 2009 at 08:43 PM. Reason: Matrix mult was in the wrong order
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: December 2nd 2010, 03:40 PM
  2. Matrix Problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 22nd 2010, 11:26 PM
  3. matrix problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 18th 2008, 10:46 AM
  4. Help with Matrix Problem
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: October 26th 2008, 05:57 PM
  5. Another matrix problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 27th 2007, 08:36 AM

Search Tags


/mathhelpforum @mathhelpforum