Program calculate determinant of matrices in matlab?

Answer 1

d = det(X) returns the determinant of the square matrix X. If X contains only integer entries, the result d is also an integer.

The determinant is computed from the triangular factors obtained by Gaussian elimination [L,U] = lu(A)

s = det(L) % This is always +1 or -1

det(A) = s*prod(diag(U))

The statement A = [1 2 3; 4 5 6; 7 8 9]

produces A =

1 2 3

4 5 6

7 8 9

This happens to be a singular matrix, so d = det(A) produces d = 0. Changing A(3,3) with A(3,3) = 0 turns A into a nonsingular matrix. Now d = det(A) produces d = 27.

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http://www.mathworks.com/access/helpdesk/help/techdoc/ref/det.html