# Math 2270-3
# Maple Project I
# 
# Part A:  some matrix algebra questions
# (These questions are modified from problems on page 27 of the text
# Multivariable Mathematics with Maple, by J.A. Carlson and J.M
# Johnson.)  You are to create a document in which you answer the
# following questions, via a mixture of Maple computations and textual
# insertions.  You are to print out a copy of this document to hand in. 
# Don't forget to put your name on it! 
#       Define    

                               [1    2    3]
                               [           ]
                          A := [4    5    6]
                               [           ]
                               [7    8    9]



                               [2    1    0]
                               [           ]
                          B := [1    2    1]
                               [           ]
                               [0    1    2]

# 
# 1a)  Compute AB and BA.  Are they the same?
# 1b)  Compute A+B and B+A.  Are they the same?
# 1c)  Define C to be A+B.  Compute C^2 and compare it to A^2 + 2AB +
# B^2.  Are they the same?  Can you think of a small change you could
# make in the expression ``A^2 + 2AB + B^2'' in order to make it equal
# to C^2?  Justify your answers!
# 1d)  Define v=(1,2,3) to be a vector.  Compute Av.  What does Maple
# give you when you try vA?
# 1e)  Solve Bx=v for x, where v is the vector in (1d).  Get your
# solution all three ways that were indicated above:  by row-reducing
# the augmented matrix, by using the command ``linsolve'', and by using
# the inverse matrix to B.
# 
# 2a) Solve Ax=v for x, where A and v are as indicated above.  Verify,
# with Maple, that your solution x actually solves the equation Ax=v.
# 2b)  Repeat your work above in order to solve Ax=w, where w=(-1,4,1). 
# Explain your answer.
# 
# Part  B:  reflections
# Work through the worksheet "2270vec.mws."  This worksheet goes through
# the process of adding vectors in 2D and executes code for projecting
# vectors in 2D.  Note how there is code to visualize the projection. 
# Try inputting some different vectors in to see how additions and
# projections work.  Your task for this part is to write a Maple
# Worksheet that takes a vector in 2D and reflects it about a line in
# the coordinate plane and then visualizes this projection. Feel free to
# use any vector to test and debug your program. Make sure you put the
# appropriate text comments into your file so that I can understand it.
#