Laplace expansion (1/2)
Laplace expansion is an alternative way to compute determinants. Essentially, a Laplace expansion is an alternating sum of the entries in a row or column multiplied by the determinant of the matrix obtained by deleting the corresponding row and column (i.e. a minor of the matrix). The determinant of the (i,j) minor times (-1)^(i+j) is called the (i,j) cofactor of the matrix, so Laplace expansion is also often referred to as cofactor expansion. Cofactor expansion can be derived using permutation expansions, though we won't discuss that here.
Laplace expansion is usually most useful when computing determinants of matrices with lots of zeros (which you might come across more often than you think!). However, the row reduction method to computing determinants is often more time efficient than Laplace expansion, so deciding which method will be quicker or more useful can be pretty situational.
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