### Related

##### beta-coefmatrix-echelon-rank-row-transpose

eq1:x=lambda+alpha+beta;

eq2:y=lambda-alpha+3*...

eq3:z=lambda+2*alpha;

Calculate

##### echelon-matrix

M: matrix ([1,2,3],[3...

A: echelon (M);

A .[x,y,1];

Calculate

##### echelon-matrix-rank-row

v1:[1,0,2];

v2:[-2,1,1];

v3:[0,1,5];

Calculate

x: matrix([1], [0], [...

y: matrix([0], [1], [...

z: matrix([0], [0], [...

Calculate

##### echelon-matrix

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

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

m:matrix(v1,v2);

Calculate

ptA_src: [234.9146728...

ptB_src: [970.0684814...

ptC_src: [239.5346679...

Calculate

##### beta-diff-exp-freeof-log-ratsimp

freeof(ratsimp(diff((...

display_format_intern...

Calculate

##### coefmatrix-eliminate-length-makelist-rank-triangularize

eqlist: [wu-wt,2*wu-w...

m: coefmatrix(makelis...

triangularize(m);

Calculate

##### beta-cos-expand-sin

eq1: sin(gama) = (a *...

eq2: R*(1 - eq1^2) = ...

expand(eq2);

Calculate

##### echelon-genmatrix-invert-lambda-random

invert(echelon(genmat...

Calculate

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
[ - 1  - 1  - 1 ]
[               ]
[ - 1   1   - 3 ]
(%o5)                          [               ]
[ - 1  - 2   0  ]
[               ]
[ - 2  - 3  - 1 ]
(%o6)                                  2
[ - 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 ]
[ - 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 ]
[ - 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 ]
[ - 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) ```

### Related Help

Help for Beta

Help for Coefmatrix

Help for Echelon

Help for Rank

Help for Row

Help for Transpose