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determinant-matrix-permanent

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

permanent(a);

determinant(a);

Calculate

determinant-factor-matrix-resultant-subst

b0:a1*c0-a0*c1;

b1:a2*c0-a0*c2;

b2:a3*c0-a0*c3;

Calculate

determinant-matrix-permanent

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

permanent(a);

determinant(a);

Calculate

solve

eq1:-g^2*b^2+a^2*g2^2...

eq2:b^2+a^2*g3^2/c^2-...

eq3:a^2*g1^2-b1^2*c^2...

Calculate

solve

solve(x^2/(2-x)=2,x);

Calculate

solve

T:A=(D*E*F*G)*(B-C) -...

solve(T,A);

Calculate

determinant-invert-matrix

a:matrix([a,b],[c,d]);

b:matrix([e,f],[g,h]);

a.b;

Calculate

solve

eq1:(D+E-C)^2+D^2=4;

eq2:C^2+D^2=9;

eq3:C^2+E^2=16;

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,row,solve]

Run Example
(%i1)uk_row: [x1-2*x2+3*x3-x4=-2, 3*x1+x2-x3+2*x4=9, -3*x1-2*x2+x3+2*x4=-13, 2*x1-2*x2+x3-x4=5];
(%o1) [- x4 + 3 x3 - 2 x2 + x1 = - 2, 2 x4 - x3 + x2 + 3 x1 = 9, 
                   2 x4 + x3 - 2 x2 - 3 x1 = - 13, - x4 + x3 - 2 x2 + 2 x1 = 5]
(%i2) solve(uk_row,[x1,x2,x3,x4]);
(%o2)               [[x1 = 3, x2 = 0, x3 = - 2, x4 = - 1]]
(%i3) a: matrix[[1,-2,3,-1],[3,1,-1,2],[-3,-2,1,2],[2,-2,1,-1]];
(%o3) 
     matrix
           [1, - 2, 3, - 1], [3, 1, - 1, 2], [- 3, - 2, 1, 2], [2, - 2, 1, - 1]
(%i4) determinant(a);
(%o4)                                 75
(%i5) 
Run Example
uk_row: [2*x1+3*x2-2*x3+x4=3, -2*x1+x2-x3+2*x4=9, x1-2*x2+3*x3-x4=-12, 3*x1+x2-2*x3-x4=-1];
(%o1) [x4 - 2 x3 + 3 x2 + 2 x1 = 3, 2 x4 - x3 + x2 - 2 x1 = 9, 
                 - x4 + 3 x3 - 2 x2 + x1 = - 12, - x4 - 2 x3 + x2 + 3 x1 = - 1]
(%i2) solve(uk_row,[x1,x2,x3,x4]);
(%o2)               [[x1 = - 2, x2 = 0, x3 = - 3, x4 = 1]]
(%i3) a: matrix[[2,3,-2,1],[-2,1,-1,2],[1,-2,3,-1],[3,1,-2,-1]];
(%o3) 
     matrix
           [2, 3, - 2, 1], [- 2, 1, - 1, 2], [1, - 2, 3, - 1], [3, 1, - 2, - 1]
(%i4) determinant(a);
(%o4)                                 16
(%i5) 
Run Example
uk_row: [3*x1+x2-2*x3-x4=-12, -2*x1+x2-x3+x4=3, x1-2*x2-x3+3*x4=-8, -3*x1+2*x2+x3-2*x4=13];
(%o1) [- x4 - 2 x3 + x2 + 3 x1 = - 12, x4 - x3 + x2 - 2 x1 = 3, 
                   3 x4 - x3 - 2 x2 + x1 = - 8, - 2 x4 + x3 + 2 x2 - 3 x1 = 13]
(%i2) solve(uk_row,[x1,x2,x3,x4]);
(%o2)               [[x1 = - 3, x2 = 0, x3 = 2, x4 = - 1]]
(%i3) a: matrix[[3,1,-2,-1],[-2,1,-1,1],[1,-2,-1,3],[-3,2,1,-2]];
(%o3) 
   matrix
         [3, 1, - 2, - 1], [- 2, 1, - 1, 1], [1, - 2, - 1, 3], [- 3, 2, 1, - 2]
(%i4) determinant(a);
(%o4)                                  4
(%i5) 
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