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Laplace's theorem


The determinant of a square matrix M = aijmxn can be obtained by summing the products of the elements of any row (row or column) of the matrix M by their cofactors.

So setting we have:

on what is the sum of all index terms iranging from 1 to m, .

Example:

Calculate the determinant of matrix A by applying the Laplace Theorem:

Highlighting the second line of the matrix, we have D = 5. THE21 + 0. THE22 + 1. THE23 + (-3). THE24. Let's calculate the cofactors:

Finally, we calculate the determinant:

D = 5. THE21 + 0. THE22 + 1. THE23 + 3. THE24
D = 5. (-411) + 0. (462) + 1. (60) + (-3). (-399)
D = -2055 + 0 + 60 + 1197
D = - 798

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