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adjoint-determinant-matrix-transpose

a:matrix([a_1],[a_2],...

t:matrix([0,-a_3,a_2,...

m:matrix([0,-a_3,a_2,...

Calculate

adjoint-determinant-invert-matrix

r1:[15,-3,-1];

r2:[-3,18,-6];

r3:[-4,-1,12];

Calculate

adjoint-determinant-expand-matrix

A:matrix([z-3.98,5.94...

determinant(A);

adjoint(A);

Calculate

adjoint-determinant-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-matrix-transpose

a:-(k1+k2+k3)/m1;

b:k2/m1;

c:k3/m1;

Calculate

adjoint-determinant-invert-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-cos-matrix-sin

B : matrix([cos(18),-...

C : adjoint(B);

Calculate

adjoint-determinant-expand-matrix-transpose

A:matrix([z-3.98,5.94...

B:matrix([1,0,0,0]);

C:matrix([3.117264198...

Calculate

adjoint-determinant-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint

Run Example
(%i1)A:matrix([z-3.98,5.94,-3.94,0.98],[-1,z,0,0],[0,-1,z,0],[0,0,-1,z]);
                       [ z - 3.98  5.94  - 3.94  0.98 ]
                       [                              ]
                       [   - 1      z      0      0   ]
(%o1)                  [                              ]
                       [    0      - 1     z      0   ]
                       [                              ]
                       [    0       0     - 1     z   ]
(%i2) B:matrix([1],[0],[0],[0]);
                                     [ 1 ]
                                     [   ]
                                     [ 0 ]
(%o2)                                [   ]
                                     [ 0 ]
                                     [   ]
                                     [ 0 ]
(%i3) C:matrix([3.11726419816378e-10,2.33794819592328e-12,3.10175580877909e-10,7.75429210802766e-13]);
(%o3)  Col 1 = [ 3.11726419816378E-10 ] Col 2 = [ 2.3379481959232799E-12 ]
          Col 3 = [ 3.1017558087790898E-10 ] Col 4 = [ 7.7542921080276605E-13 ]
(%i4) sol:determinant(A);
                                3         2
(%o4)               (z - 3.98) z  + 5.94 z  - 3.94 z + 0.98
(%i5) expand(sol);
                     4         3         2
(%o5)               z  - 3.98 z  + 5.94 z  - 3.94 z + 0.98
(%i6) transpose(adjoint(A))*sol;
               3              3         2
(%o6) matrix([z  ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
 2              3         2
z  ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
               3         2
z ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
            3         2
(z - 3.98) z  + 5.94 z  - 3.94 z + 0.98], 
          2                               3         2
[(- 5.94 z  + 3.94 z - 0.98) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
            2              3         2
(z - 3.98) z  ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                          3         2
(z - 3.98) z ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                        3         2
(z - 3.98) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98)], 
        2                        3         2
[(3.94 z  - 0.98 z) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                             3         2
(3.94 z - 0.98) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
             2                        3         2
((z - 3.98) z  + 5.94 z) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                                   3         2
((z - 3.98) z + 5.94) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98)], 
         2              3         2
[- 0.98 z  ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                      3         2
- 0.98 z ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
                    3         2
- 0.98 ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98), 
             2                               3         2
((z - 3.98) z  + 5.94 z - 3.94) ((z - 3.98) z  + 5.94 z  - 3.94 z + 0.98)])
(%i7) 
Run Example
kill(all);
(%o0)                                done
(%i1) depend(x_1,s);
(%o1)                           depend(x_1, s)
(%i2) depend(x_2,s);
(%o2)                           depend(x_2, s)
(%i3) M: matrix([m_1, 0],[0, m_2]);
                                 [ m_1   0  ]
(%o3)                            [          ]
                                 [  0   m_2 ]
(%i4) C: matrix([c_1+c_2, -c_2],[-c_2, c_2]);
                             [ c_2 + c_1  - c_2 ]
(%o4)                        [                  ]
                             [   - c_2     c_2  ]
(%i5) K: matrix([k_1+k_2, -k_2],[-k_2, k_2]);
                             [ k_2 + k_1  - k_2 ]
(%o5)                        [                  ]
                             [   - k_2     k_2  ]
(%i6) F: matrix([F_1(s)],[F_2(s)]);
                                  [ F_1(s) ]
(%o6)                             [        ]
                                  [ F_2(s) ]
(%i7) X: matrix([x_1(s)],[x_2(s)]);
                                  [ x_1(s) ]
(%o7)                             [        ]
                                  [ x_2(s) ]
(%i8) dotdistrib: true;
(%o8)                                true
(%i9) eqn: F = M.(s^2*X) + C.(s*X) + K.X;
      [ F_1(s) ]                                              2
(%o9) [        ] = matrix([- c_2 s x_2(s) - k_2 x_2(s) + m_1 s  x_1(s)
      [ F_2(s) ]
 + (c_2 + c_1) s x_1(s) + (k_2 + k_1) x_1(s)], 
      2
[m_2 s  x_2(s) + c_2 s x_2(s) + k_2 x_2(s) - c_2 s x_1(s) - k_2 x_1(s)])
(%i10) Z: mat_unblocker(matrix([coeff(rhs(eqn),x_1(s)), coeff(rhs(eqn),x_2(s))]));
         [      2                                                   ]
         [ m_1 s  + (c_2 + c_1) s + k_2 + k_1     - c_2 s - k_2     ]
(%o10)   [                                                          ]
         [                                          2               ]
         [           - c_2 s - k_2             m_2 s  + c_2 s + k_2 ]
(%i11) H: invert(Z);
                     2                       2
(%o11) matrix([(m_2 s  + c_2 s + k_2)/((m_1 s  + (c_2 + c_1) s + k_2 + k_1)
       2
 (m_2 s  + c_2 s + k_2) + (- c_2 s - k_2) (c_2 s + k_2)), 
                     2                                    2
(c_2 s + k_2)/((m_1 s  + (c_2 + c_1) s + k_2 + k_1) (m_2 s  + c_2 s + k_2)
 + (- c_2 s - k_2) (c_2 s + k_2))], [(c_2 s + k_2)
        2                                    2
/((m_1 s  + (c_2 + c_1) s + k_2 + k_1) (m_2 s  + c_2 s + k_2)
                                         2
 + (- c_2 s - k_2) (c_2 s + k_2)), (m_1 s  + (c_2 + c_1) s + k_2 + k_1)
        2                                    2
/((m_1 s  + (c_2 + c_1) s + k_2 + k_1) (m_2 s  + c_2 s + k_2)
 + (- c_2 s - k_2) (c_2 s + k_2))])
(%i12) N: adjoint(Z);
         [      2                                                   ]
         [ m_2 s  + c_2 s + k_2             c_2 s + k_2             ]
(%o12)   [                                                          ]
         [                            2                             ]
         [     c_2 s + k_2       m_1 s  + (c_2 + c_1) s + k_2 + k_1 ]
(%i13) d: determinant(Z);
             2                                    2
(%o13) (m_1 s  + (c_2 + c_1) s + k_2 + k_1) (m_2 s  + c_2 s + k_2)
                                                                              2
                                                             - (- c_2 s - k_2)
(%i14) 
Run Example
m:matrix([-3,5,6],[-1,2,2],[1,-1,-1]);
                               [ - 3   5    6  ]
                               [               ]
(%o1)                          [ - 1   2    2  ]
                               [               ]
                               [  1   - 1  - 1 ]
(%i2) adjoint(m);
                               [  0   - 1  - 2 ]
                               [               ]
(%o2)                          [  1   - 3   0  ]
                               [               ]
                               [ - 1   2   - 1 ]
(%i3) 

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