Matrices

 

In Reduce

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Mathematica

matrix xx,yy;

let xx= mat((a11,a12),(a21,a22)), yy= mat((y1),(y2));

xx;

    [a11  a12]
    [        ]
    [a21  a22]

det xx;

    a11*a22 - a12*a21

zz:= xx**(-1)*yy;

          [  - a12*y2 + a22*y1 ]
          [--------------------]
          [ a11*a22 - a12*a21  ]
    zz := [                    ]
          [  a11*y2 - a21*y1   ]
          [------------------- ]
          [ a11*a22 - a12*a21  ]

1/xx**2;

                                    2
                       a12*a21 + a22
    mat((-------------------------------------------,
             2    2                          2    2
          a11 *a22  - 2*a11*a12*a21*a22 + a12 *a21

                      - a12*(a11 + a22)
         -------------------------------------------),
             2    2                          2    2
          a11 *a22  - 2*a11*a12*a21*a22 + a12 *a21

                      - a21*(a11 + a22)
        (-------------------------------------------,
             2    2                          2    2
          a11 *a22  - 2*a11*a12*a21*a22 + a12 *a21

                          2
                       a11  + a12*a21
         -------------------------------------------))
             2    2                          2    2
          a11 *a22  - 2*a11*a12*a21*a22 + a12 *a21

mateigen(mat((2,-1,1),(0,1,1),(-1,1,1)),et);

    {{et - 1,2,

      [arbcomplex(13)]
      [              ]
      [arbcomplex(13)]
      [              ]
      [      0       ]

      },

     {et - 2,1,

      [      0       ]
      [              ]
      [arbcomplex(14)]
      [              ]
      [arbcomplex(14)]

      }}