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echelon-matrix-row-transpose

v1:[1,2,0,1];

v2:[x,y,z,t];

m:matrix(v1,v2);

Calculate

echelon-matrix-row

/*Creamos una matriz ...

/*Del ejercicio anter...

p:echelon(n);

Calculate

echelon-matrix-row

v1:[1,0,2];

v2:[2,1,1];

v3:[0,1,5];

Calculate

echelon-matrix-row-transpose

v1:[1,2,0,1];

v2:[x,y,z,t];

m:matrix(v1,v2);

Calculate

echelon-matrix-row

/*Creamos una matriz ...

/*Del ejercicio anter...

p:echelon(n);

Calculate

echelon-matrix-row-transpose

v1:[1,2,0,1];

v2:[x,y,z,t];

m:matrix(v1,v2);

Calculate

echelon-matrix-row-transpose

v1: [1,2/3,1/3,0,1/3];

v2: [0,1,-1,-2,-3];

v3: [0,0,1,5/3,7/3];

Calculate

echelon-matrix-row-transpose

v1: [1,2/3,1/3,0,1/3];

v2: [0,1,-1,-2,-3];

v3: [0,0,1,5/3,7/3];

Calculate

echelon-matrix-row

v1:[1,0,2];

v2:[2,1,1];

v3:[0,1,5];

Calculate

echelon-matrix-row-transpose

v1: [1,2/3,1/3,0,1/3];

v2: [0,1,-1,-2,-3];

v3: [0,0,1,5/3,7/3];

Calculate

[echelon,matrix,row]

Run Example
(%i1)v1:[1,0,2];
(%o1)                              [1, 0, 2]
(%i2) v2:[2,1,1];
(%o2)                              [2, 1, 1]
(%i3) v3:[0,1,5];
(%o3)                              [0, 1, 5]
(%i4) m:matrix(v1,v2,v3);
                                  [ 1  0  2 ]
                                  [         ]
(%o4)                             [ 2  1  1 ]
                                  [         ]
                                  [ 0  1  5 ]
(%i5) Rank(m);
                                    [ 1  0  2 ]
                                    [         ]
(%o5)                          Rank([ 2  1  1 ])
                                    [         ]
                                    [ 0  1  5 ]
(%i6) n:echelon(m);
                                 [ 1  0   2  ]
                                 [           ]
(%o6)                            [ 0  1  - 3 ]
                                 [           ]
                                 [ 0  0   1  ]
(%i7) w1:row(n,1);
(%o7)                             [ 1  0  2 ]
(%i8) w2:row(n, 2);
(%o8)                            [ 0  1  - 3 ]
(%i9) w3:row(n,3);
(%o9)                             [ 0  0  1 ]
(%i10) 
Run Example
/*Creamos una matriz con los vectores del generador, para despues triangularla con Gauss y saber cual es la base del subespacio*/m:matrix([1,1,0,1],[1,2,-1,1],[1,-1,1,1],[1,1,2,-a]);
                             [ 1   1    0    1  ]
                             [                  ]
                             [ 1   2   - 1   1  ]
(%o1)                        [                  ]
                             [ 1  - 1   1    1  ]
                             [                  ]
                             [ 1   1    2   - a ]
(%i2) /*Del ejercicio anterior sabemos que si a=-1 el rango de la matriz será 3, por lo tanto dimensión 3, y si a es distinto de -1 el rango será 4, y la dimensión del subespacio será 4.Veamos una base si a=-1, usando Gauss para triangular.*/n:matrix([1,1,0,1],[1,2,-1,1],[1,-1,1,1],[1,1,2,1]);
                              [ 1   1    0   1 ]
                              [                ]
                              [ 1   2   - 1  1 ]
(%o2)                         [                ]
                              [ 1  - 1   1   1 ]
                              [                ]
                              [ 1   1    2   1 ]
(%i3) p:echelon(n);
                               [ 1  1   0   1 ]
                               [              ]
                               [ 0  1  - 1  0 ]
(%o3)                          [              ]
                               [ 0  0   1   0 ]
                               [              ]
                               [ 0  0   0   0 ]
(%i4) /*Las filas de la matriz conformarían una base (w1,w2,w3)*/w1:row(p,1);
(%o4)                           [ 1  1  0  1 ]
(%i5) w2:row(p,2);
(%o5)                          [ 0  1  - 1  0 ]
(%i6) w3:row(p,3);
(%o6)                           [ 0  0  1  0 ]
(%i7) 
Run Example
v1:[1,0,2];
(%o1)                              [1, 0, 2]
(%i2) v2:[2,1,1];
(%o2)                              [2, 1, 1]
(%i3) v3:[0,1,5];
(%o3)                              [0, 1, 5]
(%i4) m:matrix(v1,v2,v3);
                                  [ 1  0  2 ]
                                  [         ]
(%o4)                             [ 2  1  1 ]
                                  [         ]
                                  [ 0  1  5 ]
(%i5) Rank(m);
                                    [ 1  0  2 ]
                                    [         ]
(%o5)                          Rank([ 2  1  1 ])
                                    [         ]
                                    [ 0  1  5 ]
(%i6) n:echelon(m);
                                 [ 1  0   2  ]
                                 [           ]
(%o6)                            [ 0  1  - 3 ]
                                 [           ]
                                 [ 0  0   1  ]
(%i7) w1:row(n,1);
(%o7)                             [ 1  0  2 ]
(%i8) w2:row(n, 2);
(%o8)                            [ 0  1  - 3 ]
(%i9) w3:row(n,3);
(%o9)                             [ 0  0  1 ]
(%i10) nma:matrix([1,0,2], [0,1,-3],[0,0,1],[x,y,z]);
                                 [ 1  0   2  ]
                                 [           ]
                                 [ 0  1  - 3 ]
(%o10)                           [           ]
                                 [ 0  0   1  ]
                                 [           ]
                                 [ x  y   z  ]
(%i11) 
[abs,acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,acos,asin,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,floor,fullmap,matrix,mod,numer,transpose] [abs,floor,matrix,mod,numer,simp,transpose] [acos,asin,atan,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt] [acos,float,matrix,sqrt] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,beta,coefmatrix,echelon,rank,row,transpose] [addcol,bfloat,echelon,fpprec,fpprintprec,load,matrix,rowop] [addcol,echelon,ident,matrix,transpose] [addcol,echelon,ident,matrix] [addcol,echelon,matrix,transpose] [addrow,ev,log,matrix] [adjoint,determinant,invert,matrix] [adjoint,determinant,matrix] [allroots,at,charpoly,float,lambda,matrix,solve] [allroots,determinant,matrix] [args,divisors,lreduce,matrix,subst] [assume,expand,matrix,subst] [beta,coefmatrix,echelon,rank,row,transpose] [beta,coefmatrix,echelon,rank,row] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [charpoly,matrix] [col,echelon,length,matrix] [col,length,matrix,matrixp,rest,row,transpose] [determinant,echelon,linsolve,matrix,rank] [determinant,echelon,matrix,permanent] [determinant,echelon,matrix,rank,row] [determinant,echelon,matrix,rank,transpose] [determinant,echelon,matrix,rank] [determinant,echelon,matrix] [echelon,eliminate,matrix,triangularize] [echelon,integrate,matrix,partfrac,rank,submatrix] [echelon,kill,matrix,transpose] [echelon,linsolve,matrix,rank] [echelon,linsolve,matrix,transpose] [echelon,matrix,rank,row,transpose] [echelon,matrix,rank,row] [echelon,matrix,rank,transpose] [echelon,matrix,rank] [echelon,matrix,row,transpose] [echelon,matrix,row] [echelon,matrix,transpose] [echelon,matrix] [exp,lhs,linsolve,matrix,rhs,row,subst] [exp,lhs,linsolve,matrix,rhs,row] [exp,lhs,matrix,rhs,row,solve] [invert,load,matrix,ratsimp,row,solve] [invert,load,matrix,row]

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