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Math Help - Help with Matrix equation

  1. #1
    Junior Member
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    Help with Matrix equation

    Hello,

    I'm asked to solve for X

    I have; AX = 2X + C

    A =<br />
\begin{matrix} 3 & -1  \\ 1 & 2  \\<br />
 \end{matrix}<br /> <br />

    C =<br />
\begin{matrix}<br />
  1 & 2 & 0 \\<br />
  0 &-1 & 1  \\<br />
 \end{matrix}<br /> <br />

    I have an answer but it looks wrong (not very attractive numbers)

    What I've done is solve for X

    X = C /(A-2) or X=-0.5 (A^-1)(C)

    but I think here is where I am going wrong, I also calculated the determinant of A and adj(A) to find the inverse but my numbers are like 0.286 0.143 etc

    any help would be appreciated


    ---

    EDIT: Sorry the matrix messed up in Latex but its still visible
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  2. #2
    MHF Contributor
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    Re: Help with Matrix equation

    Hey entrepreneurforum.co.uk.

    Given you have AX = 2X + C you can get (A-2I)X = C which implies X = (A-2I)^(-1)*C.

    Try calculating (A-2I)^(-1) and see what you get for that.

    Note that you can't do what you did (divide by a matrix): you can only pre-multiply or post-multiply and in this particular instance, you need to post multiply since Y^(-1)*Y = I.
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  3. #3
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    Re: Help with Matrix equation

    An alternative to the matrix inversion method is to see that X is 2 by 3, calling its elements a,b,c,d,e,f, say, substituting in on both sides of the equation, simplifying, and equating corresponding elements.
    The resulting equations solve easily.
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Help with Matrix equation

    Quote Originally Posted by entrepreneurforum.co.uk View Post
    A = \begin{matrix} 3 & -1 \\ 1 & 2 \\
    \end{matrix}

    C =
    \begin{matrix}
    1 & 2 & 0 \\
    0 &-1 & 1 \\
    \end{matrix}
    A quick LaTeX tip: You are using |...the format is \ for the coding. Similarly use \\ between lines of the matrix. It is also a good idea to put everything on one line.
    For example:
    [tex]A = \left ( \begin{matrix} 3 & -1 \\ 1 & 2 \end{matrix} \right )[/tex]
    gives
    A = \left ( \begin{matrix} 3 & -1 \\ 1 & 2 \end{matrix} \right )

    Likewise the matrix for C is:
    C = \left ( \begin{matrix} 1 & 2 & 0 \\ 0 & -1 & 1 \end{matrix} \right )

    -Dan
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