% exercise 1.1 in Tref&Bau
B = 6*hilb(4)  % make a convenient 4x4 example;
               %   many other ways o.k. but rand() is inconvenient---why?
% part (a)
% MATRIX:                    ACTION ON B:
  M1 = diag([2 1 1 1]);      B*M1
  M2 = diag([1 1 .5 1]);     M2*B*M1
  M3 = [1 0 1 0;
        0 1 0 0;
        0 0 1 0;
        0 0 0 1];            M3*M2*B*M1
  M4 = [0 0 0 1;
        0 1 0 0;
        0 0 1 0;
        1 0 0 0];            M3*M2*B*M1*M4
  M5 = [1 -1  0  0;
        0  1  0  0;
        0 -1  1  0;
        0 -1  0  1];         M5*M3*M2*B*M1*M4
  M6 = [1 0 0 0;
        0 1 0 0;
        0 0 1 1;
        0 0 0 0];            M5*M3*M2*B*M1*M4*M6
  M7 = [0 0 0;
        1 0 0;
        0 1 0;
        0 0 1];              M5*M3*M2*B*M1*M4*M6*M7
% part (b)
A = M5*M3*M2;
C = M1*M4*M6*M7;             A*B*C
% morals drawn from exercise 1.1:
%   1.  All seven operations *can* be written as matrix multiplication.
%   2.  Matrix multiplication is associative so I don't need lots
%       of parentheses (though initially I had them ...).
%   3.  Column ops on the right, row ops on the left.
%   4.  It is nice to both use the command line *and* have a script
%       to do a job of even this modest complexity.