07-Jan-2022 21:50:23

i4mat_rref2_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  i4mat_rref2() computes the reduced row echelon form of
  an augmented integer matrix.

  Test 1, just get the IRREF.

  Matrix A:

  Col:       1        2        3        4        5        6        7  
  Row

    1:       1        3        0        2        6        3        1  
    2:      -2       -6        0       -2       -8        3        1  
    3:       3        9        0        0        6        6        2  
    4:      -1       -3        0        1        0        9        3  

  A has rank 3

  RREF of A:

  Col:       1        2        3        4        5        6        7  
  Row

    1:       1        3        0        0        2        0        0  
    2:       0        0        0        1        2        0        0  
    3:       0        0        0        0        0        3        1  
    4:       0        0        0        0        0        0        0  

  Test 2, look for inconsistency.

  Matrix A:

  Col:       1        2        3        4  
  Row

    1:       1       -2        3       -1  
    2:       3       -6        9       -3  
    3:       0        0        0        0  
    4:       2       -2        0        1  
    5:       6       -8        6        0  
    6:       3        3        6        9  
    7:       1        1        2        3  

  RHS b1:

     1:      1
     2:      2
     3:      3
     4:      4
     5:      5
     6:      5
     7:      7

  RHS b2:

     1:      4
     2:     12
     3:      0
     4:      2
     5:     12
     6:      9
     7:      3
  A has rank 3

  RREF of A

  Col:       1        2        3        4  
  Row

    1:      16        0        0       29  
    2:       0       16        0       21  
    3:       0        0       16       -1  
    4:       0        0        0        0  
    5:       0        0        0        0  
    6:       0        0        0        0  
    7:       0        0        0        0  
  A|b1 has rank 4

  RREF of A|b1

  Col:       1        2        3        4        5  
  Row

    1:      16        0        0       29        0  
    2:       0       16        0       21        0  
    3:       0        0       16       -1        0  
    4:       0        0        0        0        1  
    5:       0        0        0        0        0  
    6:       0        0        0        0        0  
    7:       0        0        0        0        0  
  Linear system A*x=b1 is INCONSISTENT.
  A|b2 has rank 3

  RREF of A|b2

  Col:       1        2        3        4        5  
  Row

    1:      16        0        0       29       16  
    2:       0       16        0       21        0  
    3:       0        0       16       -1       16  
    4:       0        0        0        0        0  
    5:       0        0        0        0        0  
    6:       0        0        0        0        0  
    7:       0        0        0        0        0  
  Linear system A*x=b1 is CONSISTENT.

  Right hand side of A_rref*x_rref=b1_rref:

     1:     16
     2:      0
     3:     16
     4:      0
     5:      0
     6:      0
     7:      0

  Solution of A*x=b2:

     1:            1
     2:            0
     3:            1
     4:            0

  Test 3, inverse.

  A_inv * A:

  Col:       1             2             3             4       
  Row
      1 :           1             0             0             0  
      2 :           0             1             0             0  
      3 :           0             0             1             0  
      4 :           0             0             0             1  

i4mat_rref2_test():
  Normal end of execution.

07-Jan-2022 21:50:24