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adjoint-determinant-matrix-ratsimp-solve

a:matrix( [2,b,5],[-1...

determinant(a);

solve(determinant(a));

Calculate

adjoint-determinant-invert-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-invert-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-invert-matrix

r1:[3,0,2];

r2:[2,1,0];

r3:[-1,5,1];

Calculate

adjoint-determinant-invert-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-invert-matrix

r1:[3,2,2];

r2:[2,3,2];

r3:[1,1,1];

Calculate

adjoint-determinant-matrix-ratsimp-solve

a:matrix( [2,1,5],[-1...

determinant(a);

solve(determinant(a));

Calculate

adjoint-matrix

m:matrix([-3,5,6],[-1...

adjoint(m);

Calculate

adjoint-matrix

matrix([a,b],[0,0]);

adjoint(matrix([a,b],...

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
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) 
Run Example
r1:[3,2,2];
(%o1)                              [3, 2, 2]
(%i2) r2:[2,3,2];
(%o2)                              [2, 3, 2]
(%i3) r3:[1,1,1];
(%o3)                              [1, 1, 1]
(%i4) A:matrix(r1,r2,r3);
                                  [ 3  2  2 ]
                                  [         ]
(%o4)                             [ 2  3  2 ]
                                  [         ]
                                  [ 1  1  1 ]
(%i5) b:matrix([34],[32],[14]);
                                    [ 34 ]
                                    [    ]
(%o5)                               [ 32 ]
                                    [    ]
                                    [ 14 ]
(%i6) determinant(A);
(%o6)                                  1
(%i7) B:adjoint(A);
                               [  1    0   - 2 ]
                               [               ]
(%o7)                          [  0    1   - 2 ]
                               [               ]
                               [ - 1  - 1   5  ]
(%i8) invert(A).b;
                                     [ 6 ]
                                     [   ]
(%o8)                                [ 4 ]
                                     [   ]
                                     [ 4 ]
(%i9) 

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