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Math Help - Matrix problems

  1. #1
    Senior Member Paze's Avatar
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    Matrix problems

    Hi, I have a few matrix problems I am to solve.

    It says: Solve the following equations using matrices:

    Matrix problems-fylki.png

    I'm unfamiliar with this so I would like a hint on where to learn this. I understand what a matrix is but this seems different than normal matrices...E.g. boxes with numbers in them, lol.
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  2. #2
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    Re: Matrix problems

    Quote Originally Posted by Paze View Post
    Hi, I have a few matrix problems I am to solve.
    It says: Solve the following equations using matrices:
    Click image for larger version. 

Name:	fylki.png 
Views:	3 
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ID:	28857
    Solve {\left( {\begin{array}{rrr}  1&{ - 3}&0 \\   0&1&1 \\   2&{ - 1}& 4 \end{array}} \right)^{ - 1}}\left( {\begin{array}{r}  2 \\   { - 2} \\ { 1} \end{array}} \right)
    Thanks from Paze, topsquark and HallsofIvy
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  3. #3
    Senior Member Paze's Avatar
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    Re: Matrix problems

    Quote Originally Posted by Plato View Post
    Solve {\left( {\begin{array}{rrr}  1&{ - 3}&0 \\   0&1&1 \\   2&{ - 1}& 4 \end{array}} \right)^{ - 1}}\left( {\begin{array}{r}  2 \\   { - 2} \\ { 1} \end{array}} \right)
    Oh, I see. Thanks!
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  4. #4
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    Re: Matrix problems

    For anyone who was wondering, the original problem, x_1- 3x_2= 2, x_2+ x_3= -2, 2x_1- x_2+ 4x_3= 1 is equivalent to the matrix equation
    \begin{pmatrix}1 & -3 & 0 \\ 0 & 2 & 1 \\ 2 & -1 & 4 \end{pmatrix}\begin{pmatrix}x_1\\ x_2\\ x_3\end{pmatrix}= \begin{pmatrix}2 \\ -2 \\ 1\end{pmatrix}

    Thinking of that as "Ax= b", multiply both sides by A^{-1} to get x= A^{-1}b.
    Thanks from topsquark and Paze
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  5. #5
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    Re: Matrix problems

    Quote Originally Posted by Paze View Post
    Hi, I have a few matrix problems I am to solve.

    It says: Solve the following equations using matrices:

    Click image for larger version. 

Name:	fylki.png 
Views:	3 
Size:	4.8 KB 
ID:	28857

    I'm unfamiliar with this so I would like a hint on where to learn this. I understand what a matrix is but this seems different than normal matrices...E.g. boxes with numbers in them, lol.
    Set up your augmented matrix

    \displaystyle \begin{align*} \left[ \begin{matrix} 1 & -3 & 0 & \phantom{-}2 \\ 0 & \phantom{-}1 & 1 & -2 \\ 2 & -1 & 4 & \phantom{-}1  \end{matrix} \right] \end{align*}

    R3 - 2R1 -> R3

    \displaystyle \begin{align*} \left[ \begin{matrix} 1 & -3 & 0 & \phantom{-}2 \\ 0 &  \phantom{-}1 & 1 & -2 \\ 0 & \phantom{-}5 & 4 & -3 \end{matrix} \right] \end{align*}

    R3 - 5R2 -> R3

    \displaystyle \begin{align*} \left[ \begin{matrix} 1 & -3 & \phantom{-}0 & \phantom{-}2 \\ 0 & \phantom{-}1 & \phantom{-}1 & -2 \\ 0 & \phantom{-}0 & -1 & \phantom{-}7 \end{matrix} \right] \end{align*}

    So it can be seen that \displaystyle \begin{align*} -x_3 = 7 \implies x_3 = -7 \end{align*}. Then

    \displaystyle \begin{align*} x_2 + x_3 &= -2 \\ x_2 - 7 &= -2 \\ x_2 &= 5 \\ \\ x_1 - 3x_2 &= 2 \\ x_1 - 3(5) &= 2 \\ x_1 - 15 &= 2 \\ x_1 &= 17  \end{align*}
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