### Related

##### determinant-genmatrix-invert-lambda-log-matrix-plot2d-plot3d-transpose

plot2d((x^3+4)/(x^2),...

plot2d(['parametric, ...

plot3d(log(x^2+y^2-x*...

Calculate

##### determinant-matrix-permanent

a: matrix([0,1,1,1],[...

b: matrix([0,-1,-1,-1...

permanent(a);

Calculate

##### determinant-invert-solve-transpose

m: matrix [[8,6,5,2],...

determinant(m);

invert(m);

Calculate

v1:[1,2,1,3];

v2:[0,1,1,-5];

v3:[0,0,0,1];

Calculate

##### determinant-matrix-plot2d-solve-sqrt

m: matrix ([(-m*w*w+2...

solve(determinant(m),w);

plot2d ((sqrt(2) - 2)...

Calculate

##### determinant-matrix-triangularize

M: matrix ([3,5,2,0,-...

triangularize (M);

determinant(M);

Calculate

##### determinant-matrix-permanent

m:matrix([1,2,3,4],[5...

m1:matrix([1,2,3,4],[...

m2:matrix([1,2,3,4],[...

Calculate

##### determinant-matrix-permanent

m:matrix([1,2,3,4],[5...

m1:matrix([1,2,3,4],[...

m2:matrix([1,2,3,4],[...

Calculate

##### determinant-matrix

c:matrix([cg,-sg,0],[...

a:matrix([1,0,0],[0,c...

b:matrix([cb,0,sb],[0...

Calculate

##### determinant-matrix

M:matrix([1,2,3],[4,5...

d:determinant(M);

Calculate

### determinant

Run Example
```(%i1)factor(determinant(hessian(x*x/(v*(c-w*v)^a),[w,v])));
4
2 a (a + 1) (a v w + v w - c) x
(%o1)                  --------------------------------
2          2 a          3
v  (c - v w)    (v w - c)
(%i2) ```
Run Example
```m:matrix([cos(x),0,-sin(x)],[0,1,0],[cos(x),0,sin(x)]);
[ cos(x)  0  - sin(x) ]
[                     ]
(%o1)                       [   0     1     0     ]
[                     ]
[ cos(x)  0   sin(x)  ]
(%i2) determinant(m);
(%o2)                           2 cos(x) sin(x)
(%i3) ```
Run Example
```A:matrix([5*s+8,4],[4,12]);
[ 5 s + 8  4  ]
(%o1)                           [             ]
[    4     12 ]
(%i2) dA:determinant(A);
(%o2)                          12 (5 s + 8) - 16
(%i3) B:matrix([5*s+8,4],[(24/S)+15,24/S]);
[ 5 s + 8  4  ]
[             ]
(%o3)                           [ 24       24 ]
[ -- + 15  -- ]
[ S        S  ]
(%i4) ```

### Related Help

Help for Determinant