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Math Help - Determinant of 4 x 4 Matrix

  1. #1
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    Determinant of 4 x 4 Matrix

    If we have a 2 x 2 matrix

    \displaystyle \begin{bmatrix}a&b\\<br />
c&d\end{bmatrix}


    the determinant is given by \displaystyle ad - bc

    If we have a 3 x 3 matrix

    \displaystyle \begin{bmatrix}a&b&c\\<br />
d&e&f\\g&h&i\end{bmatrix}

    the determinant is given by aei + bfg + cdh - afh - bdi - ceg

    Is there such a formula for a 4 x 4 matrix

    \displaystyle \begin{bmatrix}a&b&c&d\\<br />
e&f&g&h\\i&j&k&l\\m&n&o&p\end{bmatrix}
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  2. #2
    MHF Contributor harish21's Avatar
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    The procedure you used to find the determinant of the 3x3 is called Sarrus' Rule. This cannot be applied to find out the determinant of a 4x4 matrix.

    You can use the method of cofactor expansion to find the determinant of a 4x4.

    This link gives you the formula for the 4x4 determinant
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