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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 260 11 
"Math 2270-2" }}{PARA 257 "" 0 "" {TEXT 261 15 "Maple Project I" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 38 "Part A: \+
 some matrix algebra questions" }}{PARA 0 "" 0 "" {TEXT -1 67 "(These \+
questions are modified from problems on page 27 of the text " }{TEXT 
258 36 "Multivariable Mathematics with Maple" }{TEXT -1 325 ", 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 an
d textual insertions.  You are to print out a copy of this document to
 hand in, as part A of your first Maple project.  Don't forget to put \+
your name and section number on it! " }}{PARA 0 "" 0 "" {TEXT -1 15 " \+
     Define   " }{TEXT 257 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"AG-%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'7%\"\"(\"\")\"\"*
" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"BG-%'matrixG6#7%7%\"\"#\"\"\"\"\"!7%F+F*F+7%F,F+F*" }}{PARA 3 "" 0 
"" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT 266 43 "1a)  Compute AB and B
A.  Are they the same?" }}{PARA 0 "" 0 "" {TEXT -1 45 "1b)  Compute A+
B and B+A.  Are they the same?" }}{PARA 0 "" 0 "" {TEXT -1 235 "1c)  D
efine C to be A+B.  Compute C^2 and compare it to A^2 + 2AB + B^2.  Ar
e they the same?  Can you think of a small change you could make in th
e expression ``A^2 + 2AB + B^2'' in order to make it equal to C^2?  Ju
stify your answers!" }}{PARA 0 "" 0 "" {TEXT -1 93 "1d)  Define v=(1,2
,3) to be a vector.  Compute Av.  What does Maple give you when you tr
y vA?" }}{PARA 0 "" 0 "" {TEXT -1 226 "1e)  Solve Bx=v for x, where v \+
is the vector in (1d).  Get your solution all three ways that were ind
icated above:  by row-reducing the augmented matrix, by using the comm
and ``linsolve'', and by using the inverse matrix to B." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 136 "2a) Solve Ax=v for \+
x, where A and v are as indicated above.  Verify, with Maple, that you
r solution x actually solves the equation Ax=v." }}{PARA 0 "" 0 "" 
{TEXT -1 91 "2b)  Repeat your work above in order to solve Ax=w, where
 w=(-1,4,1).  Explain your answer." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 24 "Part  B:  make a fractal
" }}{PARA 0 "" 0 "" {TEXT -1 525 "Create a document in which you creat
e a fractal.  You may choose to reproduce one of the more interesting \+
fractals from the class notes or chapter xeroxes, or you may create yo
ur very own.  Your document should explain the process you went throug
h to create the fractal, and should include the affine mapping picture
 (the \"L\" picture), and explanations of what each affine map does ge
ometrically.  Of course you may cut and paste the various procedures w
hich automate this process; there are links to these on our Maple page
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
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