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(3; 3)-Matrizen
Bilden Sie die inverse Matrix
(3; 3)-Matrizen
Zuerst die Determinante

 1 0 2 1 0                Teil1
 2 3 4 2 3                13 2 1 4 0

 3 0 2 3 0                Teil2
                          0 4 3 0 2 2
                          Teil3
                          2 2 0 2 3 3
     D     12
(3; 3)-Matrizen
Berechnung der Matrix B             a11   a12   a13
                                B   a21   a22   a23
                                    a31   a32   a33
        x22   x23
                                          1 0 2
        x32   x33
                                    A     2 3 4
                                          3 0 2
             3 4
 a11   det          3 2 4 0 6
             0 2
(3; 3)-Matrizen
Berechnung der Matrix B                   6   a12   a13
                                B     a21     a22   a23
        *                             a31     a32   a33
 x21         x23
                                              1 0 2
 x31         x33
                                      A       2 3 4
                                              3 0 2
             2 4
a12    det          (2 2 4 3)       ( 8) 8
             3 2
(3; 3)-Matrizen
Berechnung der Matrix B                  6    8    a13
                                 B   a21     a22   a23
                   *                 a31     a32   a33
    x21    x22
                                             1 0 2
    x31    x32
                                     A       2 3 4
                                             3 0 2
                2 3
   a13    det          2 0 3 3   9
                3 0
(3; 3)-Matrizen
Berechnung der Matrix B                         6    8     9
                                    B       a21     a22   a23
           x12   x13                        a31     a32   a33
       *
                                                    1 0 2
           x32   x33
                                            A       2 3 4
                                                    3 0 2
                 0 2
 a21       det         ( 0 2 2 0)       0
                 0 2
(3; 3)-Matrizen
Berechnung der Matrix B              6     8      9
                                 B   0     a22   a23
    x11          x13                 a31   a32   a33
            *
                                           1 0 2
    x31          x33
                                     A     2 3 4
                                           3 0 2
                1 2
   a21    det          1 2 2 3   4
                3 2
(3; 3)-Matrizen
Berechnung der Matrix B              6     8      9
                                 B   0      4 a23
   x11   x12                         a31   a32   a33
                *
                                           1 0 2
   x31   x32
                                     A     2 3 4
                                           3 0 2
               1 0
 a21     det         (1 0 0 3)   0
               3 0
(3; 3)-Matrizen
Berechnung der Matrix B                  6     8      9
                                     B   0      4    0
              x12    x13                 a31   a32   a33
              x22    x23
                                               1 0 2
         *
                                         A     2 3 4
                                               3 0 2
                   0 2
   a21       det           0 4 2 3   6
                   3 4
(3; 3)-Matrizen
Berechnung der Matrix B                  6      8     9
                                 B       0       4   0
  x11         x13                            6 a32   a33
  x21         x23
                                               1 0 2
         *
                                         A     2 3 4
                                               3 0 2
              1 2
 a21    det          (1 4 2 2)       0
              2 4
(3; 3)-Matrizen
Berechnung der Matrix B           6       8     9
                              B   0        4   0
     x11    x12                       6   0    a33
     x21    x22
                                          1 0 2
                   *
                                  A       2 3 4
                                          3 0 2
                 1 0
    a21    det         13 0 2 3
                 2 3
(3; 3)-Matrizen
Zum Schluss Matrix A-1                          6   8   9
                                            B   0   4   0
                                6   0   6       6   0   3
    1            1 T        1
A                  B            8   4   0
                12         12
                                9   0   3
                   1       1
                       0
                   2       2
            1      2   1
        A                  0
                   3   3
                  3        1
                       0
                  4        4

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Inverse matrix