determinant

The determinant of a matrix is a scalar value that can be computed from a square matrix. It is used to find the area or volume of a parallelepiped, the inverse of a matrix, and to solve systems of linear equations. The determinant of a 4×4 matrix can be computed using the following steps:

1. Find the cofactors of each element in the first row. 2. Multiply each cofactor by the corresponding element in the first row. 3. Add the products together. 4. Repeat steps 1-3 for each row in the matrix. 5. Add the results from steps 1-4.

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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:

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