Lineare Gleichungssysteme

2y+z==2,(1/2)x+3y==2,5x+2z==1

plot1=Plot3D[Solve[2y+z==2,z][[1,1,2]],{x,-5,5},{y,-5,5}]

(1/2)x+3y==2

par={0,(2/3),0}+r*({2,(1/3),0}-{0,(2/3),0})+s*({2,(1/3),1}-{0,(2/3),0})

plot2=ParametricPlot3D[par,{r,-10,10},{s,-10,10}]

plot3=Plot3D[Solve[5x+2z==1,z][[1,1,2]],{x,-5,5},{y,-5,5}]

Show[plot1,plot2,plot3]

Solve[{2y+z==2,(1/2)x+3y==2,5x+2z==1},{x,y,z}]

2x+3y+3z==-5,x+5y+(5/2)z==0,7x+21y+(27/2)z==-10

plot1=Plot3D[Solve[2x+3y+3z==-5,z][[1,1,2]],{x,-5,5},{y,-5,5}]

plot2=Plot3D[Solve[x+5y+(5/2)z==0,z][[1,1,2]],{x,-5,5},{y,-5,5}]

plot3=Plot3D[Solve[7x+21y+(27/2)z==-10,z][[1,1,2]],{x,-5,5},{y,-5,5}]

Show[plot1,plot2,plot3]

Solve[{2x+3y+3z==-5,x+5y+(5/2)z==0,7x+21y+(27/2)z==-10},{x,y,z}]

(2/3)x+4y-(3/2)z==5,(1/2)x-2y+3z==-3,(7/6)x+(26/3)y-4z==-1

plot1=Plot3D[Solve[(2/3)x+4y-(3/2)z==5,z][[1,1,2]],{x,-5,5},{y,-5,5}]

plot2=Plot3D[Solve[(1/2)x-2y+3z==-3,z][[1,1,2]],{x,-5,5},{y,-5,5}]

plot3=Plot3D[Solve[(7/6)x+(26/3)y-4z==-1,z][[1,1,2]],{x,-5,5},{y,-5,5}]

Show[plot1,plot2,plot3]

Solve[{(2/3)x+4y-(3/2)z==5,(1/2)x-2y+3z==-3,(7/6)x+(26/3)y-4z==-1},{x,y,z}]

(({{2, 1, 3, 0, 2}, {3, 0, 1, 1, 1}, {1, 2, -2, 0, 5}}))*x=(({{2}, {0}, {2}}))

A={{2,1,3,0,2},{3,0,1,1,1},{1,2,-2,0,5}}

b={{2},{0},{2}}

X={{(Subscript[x, 1])},{(Subscript[x, 2])},{(Subscript[x, 3])},{(Subscript[x, 4])},{(Subscript[x, 5])}}

Solve[A.X==b,{(Subscript[x, 1]),(Subscript[x, 2]),(Subscript[x, 3]),(Subscript[x, 4]),(Subscript[x, 5])}]

special=LinearSolve[A,b]

kern=NullSpace[A]

general=special+Transpose[kern].{λ,μ}

Solve[A.X==b,{(Subscript[x, 1]),(Subscript[x, 2]),(Subscript[x, 3]),(Subscript[x, 4]),(Subscript[x, 5])}]