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        Math 2270 Sec. 3                           Laboratory Assignment  #1.

        Treibergs                                       Due Sept. 14, 1998

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A.)     Do problems from the text, Kolman,  p.65[8,12,22,25,30,T4,T5]


B.)     (This project was inspired by problems of Multivariable Mathematics with MAPLE,         
         by J. Carlson  &  J. Johnson, p.27)

You are to create a document in which you answer the following questions, using a mixture 
of MAPLE computations and textual insertions (using Ò#Ó to comment or handwritten text.)
Print out a copy and hand it in. Remember to put your name and section number on your 
paper.

Define   
                (  2  3  4  )                 (  3  2  1  )
  A    =        (  5  6  7  ) ,       B  =    (  4  3  2  ) .
                (  8  9  0  )                 (  5  4  3  )

1.a     Compute  AB  and  BA.  Are they the same?
 .b     Compute  A + B  and  B + A.   Are they the same?
 .c     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 ÒA^2 + 2AB + B^2Ó  in order to make it equal to ÒC^2Ó?  
 .d     Compute the transpose of  AB  and compare it to the product of the transpose of  A
        and the transpose of  B  multiplied in the correct order to get equality. 
 .e     Define  v = (Ð1,2,3) to be a vector. Compute  Av.  
        What does MAPLE  give you when you try  vA?
 .f     Solve  Ax = v  in three ways where  v  is the vector in  (1.e): by row reducing 
        the augmented matrix, by using the command ÒlinsolveÓ, and by using the inverse 
        matrix of   A. (See KorevaarÕs Math2270 Project 1  handout  4d.)

2.a     Solve  Bx = w  where  B is  as above  and  w=(Ð1,Ð2,Ð3). Verify that your       
        solution solves  Bx = w.
 .b     Repeat your work in order to solve  Bx = z  where  z = (1,2,Ð3). Explain        
        your answer.