11.9.5 Determinant of a matrix with coefficients in ℤ/pℤ
In Xcas mode, Det is simply the inert form of
det; namely, it gives the determinant of a matrix without
evaluating it. (See Section 15.1.4.)
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.
-
In Maple mode, Det takes
A, a matrix with elements in ℤ/pℤ.
- Det(A) returns the determinant of A.
Example
Input in Xcas mode:
Det([[1,2,9] mod 13,[3,10,0] mod 13,[3,11,1] mod 13]) |
|
det | ⎛
⎜
⎜
⎜
⎜
⎜
⎝ |
| ⎡
⎢
⎢
⎢
⎢
⎢
⎣ | 1%13 | 2%13 | |
3%13 | | 0%13 |
3%13 | | 1%13
|
| ⎤
⎥
⎥
⎥
⎥
⎥
⎦ |
|
| ⎞
⎟
⎟
⎟
⎟
⎟
⎠ |
| | | | | | | | | | |
|
To find the value of the determinant, enter:
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:
Det([[1,2,9],[3,10,0],[3,11,1]]) mod 13 |