# Thread: Determinant of 4 x 4 Matrix

1. ## Determinant of 4 x 4 Matrix

If we have a 2 x 2 matrix

$\displaystyle \begin{bmatrix}a&b\\
c&d\end{bmatrix}$

the determinant is given by $\displaystyle ad - bc$

If we have a 3 x 3 matrix

$\displaystyle \begin{bmatrix}a&b&c\\
d&e&f\\g&h&i\end{bmatrix}$

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

Is there such a formula for a 4 x 4 matrix

$\displaystyle \begin{bmatrix}a&b&c&d\\
e&f&g&h\\i&j&k&l\\m&n&o&p\end{bmatrix}$

2. 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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# sarrus rule 4x4 matrix

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