(%i1)
solve(a-x=2*(x-b),x);
(%i2)
a:matrix([2,-1],[1,-6]);b:matrix([5,-7],[4,3]);
(%i4)
(2*b+a)/3;
(%i5)
kill(a,b);
(%i6)
A:matrix([1,-2],[3,-1]);B:matrix([2,a],[b,4]);
(%i8)
A.B=B.A;
(%i9)
solve([2-2*b=3*a+2,a-8=-a-4,6-b=b+12,3*a-4=-2*b-4],[a,b]);
(%i10)
kill(A,B);
(%i11)
matrix([2,-1],[-7,3])^^(-1);
(%i12)
matrix([2,4],[3,6])^^(-1);
(%i13)
matrix([2,-4],[3,-5])^^(-1).matrix([4,-2],[3,1]);
(%i14)
A:matrix([a,b],[c,d]);B:matrix([e,f],[g,h]);
(%i16)
(A.B)^^(-1);
(%i17)
B^^(-1).A^^(-1);
(%i18)
(A.B)^^(-1)-B^^(-1).A^^(-1);
(%i19)
ratsimp(%);
(%i20)
A:matrix([3,-2],[1,0]);
(%i21)
A^^n;
(%i22)
load(eigen);
(%i23)
eivects(A);
(%i24)
solve(determinant(A-x*matrix([1,0],[0,1]))=0,x);
(%i25)
eivals(A);
(%i26)
length(%);
(%i27)
P:matrix([1,1],[1,1/2]);
(%i28)
(P^^(-1).A.P)^n;
(%i29)
P.(P^^(-1).A.P)^n.P^^(-1);
(%i30)
kill(A,P);
(%i31)
npower(a,b,c,d):=block(
A:matrix([a,b],[c,d]),
if length(eivects(A)[2])=2 then(
l1:eivects(A)[2][1][1],l2:eivects(A)[2][2][1],
P:transpose(matrix(l1,l2)),
return(P.(P^^(-1).A.P)^n.P^^(-1))
)
else
a:eivals(A)[1][1],
return(n*a^(n-1)*A-(n-1)*a^n*matrix([1,0],[0,1]))
)$
(%i32)
npower(0,-1,4,4);
(%i33)
matrix([2,-5],[3,4])^^(-1).matrix([9],[2]);
(%i34)
determinant(matrix([a,b],[c,d]))=0;
(%i35)
matrix([-4,9],[5,8]).matrix([1,3],[2,-1])^^(-1);
(%i36)
matrix([2,-1],[5,-3])^^(-1).matrix([3],[4]);
(%i37)
Rot(th):=matrix([cos(th/180*%pi),-sin(th/180*%pi)],
[sin(th/180*%pi),cos(th/180*%pi)]);
(%i38)
Rot(60).matrix([4],[2]);
(%i39)
Rot(-60).matrix([4],[2]);
(%i40)
Rot(90);
(%i41)
matrix([-1,0],[0,1]).matrix([0,1],[1,0]);
(%i2)
lt(a,b,c,d,n):=block(
coord: setify(makelist(k,k,-1*n,n)),
points2d: listify(cartesian_product(coord,coord)),
vf2d(x,y):= vector([x,y],[(a-1)*x+b*y,c*x+(d-1)*y]),
vect2: makelist(vf2d(k[1],k[2]),k,points2d),
apply(draw2d,
append([head_length=0.1, color=blue],
vect2))
)$
(%i13)
lt-u(a,b,c,d,n):=block(
coord: setify(makelist(k,k,-1*n,n)),
points2d: listify(cartesian_product(coord,coord)),
vf2d(x,y):= vector([x,y],[(a-1)*x+b*y,c*x+(d-1)*y]),
vect2: makelist(vf2d(k[1],k[2]),k,points2d),
apply(draw2d,
append([head_length=0.1, unit_vectors=true,color=blue],
vect2))
)$