In linear algebra, the determinant is a function that takes a square matrix as an input and produces a single number as an output. The determinant is used to solve systems of linear equations, to find eigenvalues and eigenvectors of a matrix, and to compute the volume of a parallelepiped.
The determinant of a 4×4 matrix can be computed using a variety of methods. One method is to use the Laplace expansion. This method involves expanding the determinant along a row or column of the matrix. For example, to expand the determinant along the first row, we would compute the following sum:
