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echelon-matrix-transpose

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

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

m:matrix(v1,v2);

Calculate

echelon-matrix

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

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

m:matrix(v1,v2);

Calculate

echelon-matrix-rank

v1:[1,0,2];

v2:[-2,1,1];

v3:[0,1,5];

Calculate

echelon-matrix

A: matrix([1,4,69],[2...

echelon:(A);

Calculate

echelon-linsolve-matrix

eq1:x+y+z=0;

eq2:x+2*y-z+t=0;

eq3:x-y+z+t=0;

Calculate

echelon-matrix-rank

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

v1:[1,0,2];

v2:[0,0,1];

Calculate

echelon-matrix-rank-row

v1:[1,2,-1];

v2:[3,-1,0];

v3:[4,1,-1];

Calculate

echelon-matrix-rank-row

v1:[1,2,-1];

v2:[3,-1,0];

v3:[4,1,-1];

Calculate

echelon-matrix-rank

v1:[1,2,-1];

v2:[3,-1,0];

v3:[4,1,-1];

Calculate

echelon-matrix-rank-row

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

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

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

Calculate

echelon

Run Example
(%i1)A: matrix ([5,2,-1],[-1,-2,-3],[-8,-3,2],[3,-1,5]);
                               [  5    2   - 1 ]
                               [               ]
                               [ - 1  - 2  - 3 ]
(%o1)                          [               ]
                               [ - 8  - 3   2  ]
                               [               ]
                               [  3   - 1   5  ]
(%i2) echelon(A);
                                 [    2    1 ]
                                 [ 1  -  - - ]
                                 [    5    5 ]
                                 [           ]
(%o2)                            [ 0  1   2  ]
                                 [           ]
                                 [ 0  0   1  ]
                                 [           ]
                                 [ 0  0   0  ]
(%i3) 
Run Example
c:matrix([1/R1+1/R12+1/R13,-1/R12,-1/R13, I0],[-1/R12,1/R2+1/R23+1/R12,-1/R23, I0],[-1/R13,-1/R23,1/R3+1/R13+1/R23, I0]);
            [  1     1    1          1               1           ]
            [ --- + --- + --      - ---           - ---       I0 ]
            [ R13   R12   R1        R12             R13          ]
            [                                                    ]
            [        1         1    1     1          1           ]
(%o1)       [     - ---       --- + -- + ---      - ---       I0 ]
            [       R12       R23   R2   R12        R23          ]
            [                                                    ]
            [        1               1        1     1     1      ]
            [     - ---           - ---       -- + --- + ---  I0 ]
            [       R13             R23       R3   R23   R13     ]
(%i2) d:echelon(c);
                           R1 R13                     R1 R12
(%o2) matrix([1, - -----------------------, - -----------------------, 
                   (R12 + R1) R13 + R1 R12    (R12 + R1) R13 + R1 R12
     I0 R1 R12 R13
-----------------------], [0, 1, - (((R12 + R1) R23 + (R12 + R1) R13 + R1 R12)
(R12 + R1) R13 + R1 R12
 R3 + ((R12 + R1) R13 + R1 R12) R23)/((R1 R23 + (R12 + R1) R13 + R1 R12) R3), 
  ((I0 R12 + I0 R1) R13 + 2 I0 R1 R12) R23
- ----------------------------------------], 
      R1 R23 + (R12 + R1) R13 + R1 R12
[0, 0, 1, ((((I0 R13 + 3 I0 R1) R2 + (I0 R12 + I0 R1) R13 + 2 I0 R1 R12) R23
 + ((2 I0 R12 + 3 I0 R1) R13 + 3 I0 R1 R12) R2) R3)
/(((R2 + R12 + R1) R23 + (R13 + R12) R2 + (R12 + R1) R13 + R1 R12) R3
 + ((R13 + R1) R2 + (R12 + R1) R13 + R1 R12) R23
 + ((R12 + R1) R13 + R1 R12) R2)])
(%i3) fortran(d[3,4]);
      (((I0*R13+3*I0*R1)*R2+(I0*R12+I0*R1)*R13+2*I0*R1*R12)*R23+((2*I0*R
     1   12+3*I0*R1)*R13+3*I0*R1*R12)*R2)*R3/(((R2+R12+R1)*R23+(R13+R12)
     2   *R2+(R12+R1)*R13+R1*R12)*R3+((R13+R1)*R2+(R12+R1)*R13+R1*R12)*R
     3   23+((R12+R1)*R13+R1*R12)*R2)
(%o3)                                done
(%i4) e:matrix([1/R1+1/R12+1/R13,-1/R12,-1/R13, I0],[-1/R12,1/R2+1/R23+1/R12,-1/R23, 0],[-1/R13,-1/R23,1/R3+1/R13+1/R23, 0]);
            [  1     1    1          1               1           ]
            [ --- + --- + --      - ---           - ---       I0 ]
            [ R13   R12   R1        R12             R13          ]
            [                                                    ]
            [        1         1    1     1          1           ]
(%o4)       [     - ---       --- + -- + ---      - ---       0  ]
            [       R12       R23   R2   R12        R23          ]
            [                                                    ]
            [        1               1        1     1     1      ]
            [     - ---           - ---       -- + --- + ---  0  ]
            [       R13             R23       R3   R23   R13     ]
(%i5) 
Run Example
T2:matrix([-1,1,1,1,0],[-1,0,0,0,1],[-3,2,2,2,1],[-2,1,1,1,1]);
                              [ - 1  1  1  1  0 ]
                              [                 ]
                              [ - 1  0  0  0  1 ]
(%o1)                         [                 ]
                              [ - 3  2  2  2  1 ]
                              [                 ]
                              [ - 2  1  1  1  1 ]
(%i2) echelon(T2);
                              [ 1  0  0  0  - 1 ]
                              [                 ]
                              [ 0  1  1  1  - 1 ]
(%o2)                         [                 ]
                              [ 0  0  0  0   0  ]
                              [                 ]
                              [ 0  0  0  0   0  ]
(%i3) transpose(matrix([1, 0,1,0,1]));
                                     [ 1 ]
                                     [   ]
                                     [ 0 ]
                                     [   ]
(%o3)                                [ 1 ]
                                     [   ]
                                     [ 0 ]
                                     [   ]
                                     [ 1 ]
(%i4) T2.transpose(matrix([1, 0,1,0,1]));
                                     [ 0 ]
                                     [   ]
                                     [ 0 ]
(%o4)                                [   ]
                                     [ 0 ]
                                     [   ]
                                     [ 0 ]
(%i5) 
[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,echelon,rank,row,transpose] [addcol,beta,coefmatrix,echelon,rank,transpose] [addcol,bfloat,echelon,fpprec,fpprintprec,load,matrix,rowop] [addcol,echelon,ident,matrix,transpose] [addcol,echelon,ident,matrix] [addcol,echelon,matrix,transpose] [beta,coefmatrix,echelon,rank,row,transpose] [beta,coefmatrix,echelon,rank,row] [beta,coefmatrix,echelon,rank,transpose] [beta,coefmatrix,echelon,rank] [beta,echelon,kill,linsolve,matrix,rank] [block,do,echelon,fortran,matrix_size,min,return,rowop,solve] [block,do,echelon,matrix_size,min,return,rowop,solve] [block,do,echelon,matrix_size,min,return,rowop] [charpoly,echelon,eigenvectors,factor,matrix] [charpoly,echelon,eigenvectors,invert,matrix,ratsimp,solve] [coefmatrix,echelon,rank] [col,echelon,length,matrix] [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,fortran,matrix] [echelon,genmatrix,lambda,random,row] [echelon,genmatrix,lambda,random] [echelon,ident,mat_fullunblocker,matrix,submatrix,transpose,triangularize] [echelon,ident,matrix] [echelon,integrate,kill,matrix,partfrac,rank,solve,submatrix] [echelon,integrate,kill,matrix,partfrac,rank,submatrix] [echelon,integrate,matrix,partfrac,rank,submatrix] [echelon,invert,matrix] [echelon,kill,matrix,transpose] [echelon,linsolve,matrix,rank] [echelon,linsolve,matrix,transpose] [echelon,linsolve,matrix] [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,rowop] [echelon,matrix,transpose] [echelon,matrix]

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