Function Name: determinant Inputs 1. (double) An MxM matrix Outputs 1. (double) The determinant of the input matrix Banned Functions det(), eig() Function Description The determinant of a square matrix greater than 1x1 can be determined via cofactor expansion. For a 1x1 matrix, the determinant is the single element. For example, in a 3x3 a single column of the matrix is chosen. Each element of that column is called a "cofactor". There is a 2x2 sub-matrix corresponding to each cofactor. This sub-matrix is defined as all elements of the array not in the row or column of its cofactor. Note that this is always a square array. The determinants of each of these 2x2 sub-matrices are multiplied by their corresponding cofactors, and then added together to compute the overall determinant. When adding, the sign (+/-) of each cofactor is determined by the formula (-1)(cofactor row number 1) Here is an example of computing the determinant of a 3x3 matrix using cofactor expansion along the first column -d det + gx det al A-d e f break down -d e f Hence, a, d, and, g are the cofactors for each 2x2 matrix - 3 x det + 2 x det You can repeat this process each of the 2x2 matrices, performing cofactor expansion until you have only 1x1 matrices, the determinants of which are just the single value they contain Similarly, when computing the determinant of a 4x4 or larger matrix, you must recursively perform cofactor expansion until you have only 1x1 submatrices Continued