In Xcas mode, Det is simply the inert form of det; namely, it gives the determinant of a matrix without evaluating it. (See section Section 6.47.4.) In Maple mode, the Det command can additionally be used in conjunction with mod to find the determinant of a matrix whose elements are in ℤ/pℤ.
Example.
Input (in Xcas mode):
Output:
det | ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ | ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ | ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ |
To find the value of the determinant, you can enter:
Input:
Output:
5%13 |
Hence, in ℤ/13ℤ, the determinant of
A=[[1, 2, 9],[3,10,0],[3,11,1]] is 5%13 (in ℤ, det(A)=31).
Input (in Maple mode):
Output:
5 |