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echelon-matrix-rank

m:matrix([5,-1,2,7],[...

echelon(m);

rank(m);

Calculate

echelon-matrix

M: matrix ([%i,1],[1,...

A: echelon (M);

%i^2;

Calculate

echelon-matrix-rank

v1:[1,1,1,1];

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

v3:[0,-1,1,2];

Calculate

echelon-integrate-matrix-partfrac-rank-submatrix

f(x):=(5*x^2-11*x+30)...

partfrac(f(x),x);

integrate(f(x),x);

Calculate

echelon-matrix

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

echelon(a);

Calculate

transpose

F:matrix[[-3,0,1],[2,...

E;

matrix[[-3,0],[0,1],[...

Calculate

echelon-matrix

m:matrix([1,0,2],[0,0...

echelon(m);

Calculate

echelon-matrix-triangularize

eqlist: [lu-lt-l,2*lu...

m: matrix([0,-1,1,-1]...

triangularize(m);

Calculate

echelon-matrix-rank

v1:[1,2,3,4,5];

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

v3:[3,2,1,0,-1];

Calculate

[addcol,beta,coefmatrix,echelon,rank,row,transpose]

Run Example
(%i1)eq1:x=lambda+alfa+beta;
(%o1)                      x = lambda + beta + alfa
(%i2) eq2:y=lambda-alfa+3*beta;
(%o2)                     y = lambda + 3 beta - alfa
(%i3) eq3:z=lambda+2*alfa;
(%o3)                         z = lambda + 2 alfa
(%i4) eq4:t=2*lambda+3*alfa+beta;
(%o4)                    t = 2 lambda + beta + 3 alfa
(%i5) matrizasociada:coefmatrix([eq1,eq2,eq3,eq4],[lambda,alfa,beta]);
                               [ - 1  - 1  - 1 ]
                               [               ]
                               [ - 1   1   - 3 ]
(%o5)                          [               ]
                               [ - 1  - 2   0  ]
                               [               ]
                               [ - 2  - 3  - 1 ]
(%i6) rank(matrizasociada);
(%o6)                                  2
(%i7) m: transpose(matrizasociada);
                            [ - 1  - 1  - 1  - 2 ]
                            [                    ]
(%o7)                       [ - 1   1   - 2  - 3 ]
                            [                    ]
                            [ - 1  - 3   0   - 1 ]
(%i8) n: echelon(m);
                              [ 1  3   0    1  ]
                              [                ]
                              [         1    1 ]
(%o8)                         [ 0  1  - -  - - ]
                              [         2    2 ]
                              [                ]
                              [ 0  0   0    0  ]
(%i9) w1:row(n,1);
(%o9)                           [ 1  3  0  1 ]
(%i10) w2:row(n,2);
                              [         1    1 ]
(%o10)                        [ 0  1  - -  - - ]
                              [         2    2 ]
(%i11) nuevamatriz:addcol(matrizasociada,[x,y,z,t]);
                             [ - 1  - 1  - 1  x ]
                             [                  ]
                             [ - 1   1   - 3  y ]
(%o11)                       [                  ]
                             [ - 1  - 2   0   z ]
                             [                  ]
                             [ - 2  - 3  - 1  t ]
(%i12) 
Run Example
eq1:x=lambda+mu+beta;
(%o1)                       x = lambda + mu + beta
(%i2) eq2:y=lambda-mu+3*beta;
(%o2)                      y = lambda - mu + 3 beta
(%i3) eq3:z=lambda+2*mu;
(%o3)                          z = lambda + 2 mu
(%i4) eq4:t=2*lambda+3*mu +beta;
(%o4)                     t = 2 lambda + 3 mu + beta
(%i5) m1:coefmatrix([eq1,eq2,eq3,eq4],[lambda,mu,beta]);
                               [ - 1  - 1  - 1 ]
                               [               ]
                               [ - 1   1   - 3 ]
(%o5)                          [               ]
                               [ - 1  - 2   0  ]
                               [               ]
                               [ - 2  - 3  - 1 ]
(%i6) rank(m1);
(%o6)                                  2
(%i7) m1trans:transpose(m1);
                            [ - 1  - 1  - 1  - 2 ]
                            [                    ]
(%o7)                       [ - 1   1   - 2  - 3 ]
                            [                    ]
                            [ - 1  - 3   0   - 1 ]
(%i8) echelon(m1trans);
                              [ 1  3   0    1  ]
                              [                ]
                              [         1    1 ]
(%o8)                         [ 0  1  - -  - - ]
                              [         2    2 ]
                              [                ]
                              [ 0  0   0    0  ]
(%i9) m2:coefmatrix([eq1,eq2,eq3,eq4],[mu,beta]);
                                 [ - 1  - 1 ]
                                 [          ]
                                 [  1   - 3 ]
(%o9)                            [          ]
                                 [ - 2   0  ]
                                 [          ]
                                 [ - 3  - 1 ]
(%i10) m3:addcol (m2,[x,y,z,t]);
                                [ - 1  - 1  x ]
                                [             ]
                                [  1   - 3  y ]
(%o10)                          [             ]
                                [ - 2   0   z ]
                                [             ]
                                [ - 3  - 1  t ]
(%i11) w1:row(m3,1);
(%o11)                          [ - 1  - 1  x ]
(%i12) w2:row(m3,2);
(%o12)                           [ 1  - 3  y ]
(%i13) w3:row(m3,3);
(%o13)                           [ - 2  0  z ]
(%i14) w4:row(m3,4);
(%o14)                          [ - 3  - 1  t ]
(%i15) 
Run Example
eq1:x=lambda+mu+beta;
(%o1)                       x = lambda + mu + beta
(%i2) eq2:y=lambda-mu+3*beta;
(%o2)                      y = lambda - mu + 3 beta
(%i3) eq3:z=lambda+2*mu;
(%o3)                          z = lambda + 2 mu
(%i4) eq4:t=2*lambda+3*mu +beta;
(%o4)                     t = 2 lambda + 3 mu + beta
(%i5) m1:coefmatrix([eq1,eq2,eq3,eq4],[lambda,mu,beta]);
                               [ - 1  - 1  - 1 ]
                               [               ]
                               [ - 1   1   - 3 ]
(%o5)                          [               ]
                               [ - 1  - 2   0  ]
                               [               ]
                               [ - 2  - 3  - 1 ]
(%i6) rank(m1);
(%o6)                                  2
(%i7) m1trans:transpose(m1);
                            [ - 1  - 1  - 1  - 2 ]
                            [                    ]
(%o7)                       [ - 1   1   - 2  - 3 ]
                            [                    ]
                            [ - 1  - 3   0   - 1 ]
(%i8) echelon(m1trans);
                              [ 1  3   0    1  ]
                              [                ]
                              [         1    1 ]
(%o8)                         [ 0  1  - -  - - ]
                              [         2    2 ]
                              [                ]
                              [ 0  0   0    0  ]
(%i9) m2:coefmatrix([eq1,eq2,eq3,eq4],[mu,beta]);
                                 [ - 1  - 1 ]
                                 [          ]
                                 [  1   - 3 ]
(%o9)                            [          ]
                                 [ - 2   0  ]
                                 [          ]
                                 [ - 3  - 1 ]
(%i10) m3:addcol (m2,[x,y,z,t]);
                                [ - 1  - 1  x ]
                                [             ]
                                [  1   - 3  y ]
(%o10)                          [             ]
                                [ - 2   0   z ]
                                [             ]
                                [ - 3  - 1  t ]
(%i11) v1:row(m3,1);
(%o11)                          [ - 1  - 1  x ]
(%i12) v2:row(m3,2);
(%o12)                           [ 1  - 3  y ]
(%i13) v3:row(m3,3);
(%o13)                           [ - 2  0  z ]
(%i14) v4:row(m3,4);
(%o14)                          [ - 3  - 1  t ]
(%i15) m4:matrix[(v1,v2,v3)];
(%o15)                        matrix
                                    [ - 2  0  z ]
(%i16) m5:matrix[v2,v3,v4];
(%o16)        matrix
                    [ 1  - 3  y ], [ - 2  0  z ], [ - 3  - 1  t ]
(%i17) 
[abs,addcol,addrow,floor,fullmap,matrix,mod,transpose] [addcol,beta,coefmatrix,determinant,echelon,linsolve,rank,transpose] [addcol,beta,coefmatrix,determinant,echelon,rank,row,transpose] [addcol,beta,coefmatrix,determinant,echelon,rank,transpose] [addcol,beta,coefmatrix,determinant,expand,rank,transpose] [addcol,beta,coefmatrix,determinant,rank,solve,transpose] [addcol,beta,coefmatrix,determinant,rank,transpose] [addcol,beta,coefmatrix,echelon,rank,row,transpose] [addcol,beta,coefmatrix,echelon,rank,transpose] [addcol,beta,coefmatrix,rank,transpose] [addcol,bfloat,echelon,fpprec,fpprintprec,load,matrix,rowop] [addcol,coefmatrix,determinant,gamma,lambda,rank,transpose] [addcol,coefmatrix,gamma,lambda,rank,transpose] [addcol,coefmatrix,lambda] [addcol,echelon,ident,matrix,transpose] [addcol,echelon,ident,matrix] [addcol,echelon,matrix,transpose] [addcol,invert,linsolve,matrix,transpose] [addcol,matrix,transpose] [beta,coefmatrix,determinant,kill,linsolve] [beta,coefmatrix,echelon,rank,row,transpose] [beta,coefmatrix,echelon,rank,row] [beta,coefmatrix,echelon,rank,transpose] [beta,coefmatrix,echelon,rank] [beta,coefmatrix,rank,transpose] [beta,coefmatrix,rank] [beta,coefmatrix] [beta,gamma,linsolve,matrix,transpose] [ceiling,col,do,endcons,float,genmatrix,kill,makelist,min,permanent,print,random,row,sort,sqrt,transpose] [col,genmatrix,min,numer,permanent,random,row,sort,sqrt,transpose] [col,length,matrix,matrixp,rest,row,transpose] [determinant,echelon,linsolve,matrix,rank] [determinant,echelon,matrix,rank,row] [determinant,echelon,matrix,rank,transpose] [determinant,echelon,matrix,rank] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,ident,invert,matrix,rank,submatrix,transpose] [determinant,ident,invert,matrix,rank,submatrix,transpose] [echelon,integrate,matrix,partfrac,rank,submatrix] [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,transpose] [invert,matrix,rank,transpose] [matrix,nullity,nullspace,rank,transpose] [matrix,nullity,rank,sqrt,transpose]

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