d = det(X)
d = det(X) is the determinant of the square matrix X. If X contains only integer entries, the result d is also an integer.
Using det(X) == 0 as a test for matrix singularity is appropriate only for matrices of modest order with small integer entries. Testing singularity using abs(det(X)) <= tolerance is rarely a good idea because it is difficult to choose the correct tolerance. The function rcond(X) is intended to check for singular and nearly singular matrices. See rcond for details.
[L,U] = lu(A)s = +1 or -1 = det(L)det(A) = s*prod(diag(U))
A = [1 2 3; 4 5 6; 7 8 9]
produces
This happens to be a singular matrix, soA =1 2 34 5 67 8 9
d = det(A)
produces
Changingd =0
A(3,3) with
A(3,3) = 0;
turns A into a nonsingular matrix, so now
d = det(A)
produces
d =27
\,/,inv,lu,rcond,rref
(c) Copyright 1994 by The MathWorks, Inc.