
 a) Verify with numeric applications some properties. 
    
 b) The coefficients, are randomly selected by the computer.

 c) The size of the vectors, are randomly selected by the 
    computer, but you can select the size if you want.

 d) To see the result in Gnuplot (gp373w32.exe) :          

    * open the file aa2d.plt with Gnuplot.  => Gnuplot draw u and v. 
    * Press Return in Dos Windows.          => To create a new value for u.
    * Use the command Replot in Gnuplot.    => To draw the news u and v.

 
   Try the examples in this order.

    Reflection about the x-axis : 
    ===========================

                     u    = OA          : axisxa2d.c 
                     u    = AB          : axisxb2d.c
                     u[n] = AB  n < 9   : axisxc2d.c
                     u[n] = AB  n < 99  : axisxd2d.c
 
                 Triangle   ABC         : axisxe2d.c 
                 Square     ABCD        : axisxf2d.c  

    Reflection about the y-axis : 
    ===========================

                     u    = OA          : axisya2d.c 
                     u    = AB          : axisyb2d.c
                     u[n] = AB  n < 9   : axisyc2d.c
                     u[n] = AB  n < 99  : axisyd2d.c
 
                 Triangle   ABC         : axisye2d.c 
                 Square     ABCD        : axisyf2d.c  


    Reflection about the line y = x : 
    ===============================

                     u    = OA          : axisza2d.c 
                     u    = AB          : axiszb2d.c
                     u[n] = AB  n < 9   : axiszc2d.c
                     u[n] = AB  n < 99  : axiszd2d.c
 
                 Triangle   ABC         : axisze2d.c 
                 Square     ABCD        : axiszf2d.c  


    Orthogonal projection on the x-axis : 
    ===================================

                     u    = OA          : projxa2d.c 
                     u    = AB          : projxb2d.c


    Orthogonal projection on the y-axis : 
    ===================================

                     u    = OA          : projya2d.c 
                     u    = AB          : projyb2d.c



