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Math Help - Matrix problem

  1. #1
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    Matrix problem

    Question : If A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} Find C = A^T . B^T and the determinant

    Solution :

    C = \begin{bmatrix} 23 & 31 \\ 34 & 46 \end{bmatrix}.......Is this correct ???

    Determinant

    |C| = 4.............Is this correct ???
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  2. #2
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    Quote Originally Posted by zorro View Post
    Question : If A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} Find C = A^T . B^T and the determinant

    Solution :

    C = \begin{bmatrix} 23 & 31 \\ 34 & 46 \end{bmatrix}.......Is this correct ???

    Determinant

    |C| = 4.............Is this correct ???
    yes
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  3. #3
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    Quote Originally Posted by zorro View Post
    Question : If A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} Find C = A^T . B^T and the determinant

    Solution :

    C = \begin{bmatrix} 23 & 31 \\ 34 & 46 \end{bmatrix}.......Is this correct ???

    Determinant

    |C| = 4.............Is this correct ???
    A^T = \left[\begin{matrix}1 & 3\\2 & 4\end{matrix}\right]

    B^T = \left[\begin{matrix}5 & 7\\6 & 8\end{matrix}\right].


    So C = A^TB^T

     =  \left[\begin{matrix} 1 & 3\\2 & 4\end{matrix}\right]\left[\begin{matrix} 5 & 7\\6 & 8\end{matrix}\right]

     = \left[\begin{matrix}23 & 31\\34 & 46\end{matrix}\right].


    |C| = \left|\begin{matrix}23 & 31\\34 & 46\end{matrix}\right|

     = 23\cdot 46 - 31\cdot 34
    Last edited by Prove It; December 28th 2009 at 02:16 AM.
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    Thanks mite
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  5. #5
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    Quote Originally Posted by Prove It View Post
    A^T = \left[\begin{matrix}1 & 3\\2 & 4\end{matrix}\right]

    B^T = \left[\begin{matrix}5 & 7\\6 & 8\end{matrix}\right].


    So C = A^TB^T

     =  \left[\begin{matrix} 1 & 3\\2 & 4\end{matrix}\right]\left[\begin{matrix} 5 & 7\\6 & 8\end{matrix}\right]

     = \left[\begin{matrix}23 & 31\\34 & 50\end{matrix}\right].


    |C| = \left|\begin{matrix}23 & 31\\34 & 50\end{matrix}\right|

     = 23\cdot 50 - 31\cdot 34
    the last entri for matrix C is 2 \times 7 + 4 \times 8 = 14 + 32 = 46, not 50
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