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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 14 "MATH2042 3.0 W" }}{PARA 
257 "" 0 "" {TEXT -1 6 "QUIZ#1" }}{PARA 258 "" 0 "" {TEXT -1 17 "Febru
ary 13, 2003" }}{PARA 259 "" 0 "" {TEXT -1 43 "SOLUTIONS with Maple Co
mmands  and Answers." }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 2 "1." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A:=array([[3,3,1,0],[3,3,3,3],[1,1,
1,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&\"\"$
F*\"\"\"\"\"!7&F*F*F*F*7&F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "rank(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 2 "2." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 60 "A:=array([[0,1,1,-1],[3,2,-1,-1],[-2,-1,-3,
-1],[0,-1,2,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6
#7&7&\"\"!\"\"\"F+!\"\"7&\"\"$\"\"#F,F,7&!\"#F,!\"$F,7&F*F,F/F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "rowspace(A);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#<%-%'vectorG6#7&\"\"!F(\"\"\"#F)\"\"$-F%6#7&F)F(F(
#\"\"#F+-F%6#7&F(F)F(#!\"%F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 256 1 "3" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 61 "A:=array([[2,0,-1,-1],[3,-1,-3,-1],[-3,0,0,-1],[2,-2,-3,1]]);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"#\"\"!!
\"\"F,7&\"\"$F,!\"$F,7&F/F+F+F,7&F*!\"#F/\"\"\"" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "minor(
A,3,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"#\"\"!!
\"\"7%\"\"$F*F*7%F(!\"#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 262 "" 0 "" 
{TEXT -1 2 "4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "B:=array(
[[1,5,1],[-3,6,-6],[-4,1,7]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
BG-%'matrixG6#7%7%\"\"\"\"\"&F*7%!\"$\"\"'!\"'7%!\"%F*\"\"(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "eigenvals(B);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6%,(*$),&\"%t;\"\"\"*&\"\"$F(-%%sqrtG6#\"'d/KF(F(#
F(F*F(F/*&#\"#WF*F(*&F(F(*$)F&#F(F*F(!\"\"F(F7#\"#9F*F(,*F$#F7\"\"'*&#
\"#AF*F(*$)F&#F(F*F(F7F(F8F(*(^##F(\"\"#F(-F,6#F*F(,&F$F/*&#F2F*F(*$)F
&#F(F*F(F7F(F(F(,*F$F;*&F>F(*$)F&#F(F*F(F7F(F8F(*(^##F7FFF(FGF(FIF(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalf(eigenvals(B));" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+qVo'o)!\"*^$$\"+:ylcEF%$\"++Iiv^F
%^$F'$!++Iiv^F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "The eigenvalue
s are (two decimal places' approximation) : 8.69; 2.66+5.18i; 2.66-5.1
8i." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 263 "" 0 "" {TEXT -1 2 "5." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "B:=array([[-3,2,-2,2],[5/2,-
5/2,2,-2],[5/2,-9/2,4,-2],[-2,-1,1,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"BG-%'matrixG6#7&7&!\"$\"\"#!\"#F+7&#\"\"&F+#!\"&F+F+F,7&F.#!
\"*F+\"\"%F,7&F,!\"\"\"\"\"F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "eigenvects(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7%\"\"#\"\"\"<
#-%'vectorG6#7&\"\"!F+F%F%7%#!\"\"F$F%<#-F(6#7&F+F%F%F+7%F.F$<#-F(6#7&
F%F.F.F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "The eigenvectors are:
    " }{XPPEDIT 18 0 "vector([1, -1, -1, 1]);" "6#-%'vectorG6#7&\"\"\"
!\"\"F(F'" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "vector([0, 1, 1, 0]);" "6
#-%'vectorG6#7&\"\"!\"\"\"F(F'" }{TEXT -1 2 " ," }{XPPEDIT 18 0 "vecto
r([0, 0, 1, 1]);" "6#-%'vectorG6#7&\"\"!F'\"\"\"F(" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 46 "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }
}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 2 "6." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 58 "B:=array([[3,8,6,-1],[-3,2,0,3],[3,-3,-1,-3],[4,8,6
,-2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7&\"\"$
\"\")\"\"'!\"\"7&!\"$\"\"#\"\"!F*7&F*F/F-F/7&\"\"%F+F,!\"#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "charpoly(A,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,,*$)%\"xG\"\"%\"\"\"F(*&\"\"(F()F&\"\"#F(!\"\"*&\"#=F(
F&F(F(*&F,F()F&\"\"$F(F-F,F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 265 "" 
0 "" {TEXT -1 2 "7." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(
ln(x)/x^2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%#lnG6#%\"xG\"\"
\"F(!\"\"F**&F)F)F(F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 266 "" 0 "" 
{TEXT -1 2 "8." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "int(x*ln(
x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"xG\"\"#\"\"\"-%#lnG6
#F&F(#F(F'*&#F(\"\"%F(*$F%F(F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 45 "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT 257 2 "9." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "int(cos((Pi*x)/2),x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*
&\"\"\"F%%#PiG!\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 267 "" 0 "
" {TEXT -1 3 "10." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(x^(-1),x=-1..1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%$intG6$*&\"\"\"F'%\"xG!\"\"/F(;F)F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(int(x^(-1),x=-1..1));
" }}{PARA 8 "" 1 "" {TEXT -1 59 "Error, (in evalf/int) integrand has a
 pole in the interval\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "This i
ntegral does not exist." }}{PARA 0 "" 0 "" {TEXT -1 50 "%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 268 "" 0 "" 
{TEXT -1 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "h:='h':h
:=(x,y)->(x^2-y^2)^(1/2);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGR6$%\"xG%
\"yG6\"6$%)operatorG%&arrowGF)*$-%%sqrtG6#,&*$)9$\"\"#\"\"\"F6*$)9%F5F
6!\"\"F6F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(h(x,y),y);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$*&%\"yG\"\"\"*$-%%sqrtG6#,&*$)%\"xG\"\"#F&F&*$)F%F/
F&!\"\"F&F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "D[2,1](h)(
x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&%\"yG\"\"\"%\"xGF&F&*$),&
*$)F'\"\"#F&F&*$)F%F-F&!\"\"#\"\"$F-F&F0" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 51 "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 258 3 "12." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "g:='g':g:=(x,y)->sin(x-cos(y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gGR6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)-%$sinG6#,
&9$\"\"\"-%$cosG6#9%!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "D[2,1](g)(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%$sinG
6#,&%\"xG\"\"\"-%$cosG6#%\"yG!\"\"F*-F&F-F*F/" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "diff(g(x,y),y$2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&*&-%$sinG6#,&%\"xG\"\"\"-%$cosG6#%\"yG!\"\"F*)-F&F-\"\"#F*F/*&
-F,F'F*F+F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Using another co
mmand we obtain the same result:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "D[2,2](g)(x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&
*&-%$sinG6#,&%\"xG\"\"\"-%$cosG6#%\"yG!\"\"F*)-F&F-\"\"#F*F/*&-F,F'F*F
+F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 3 "13.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "int(int(exp(x)*cos(y),y
=0..Pi/4),x=0..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%%sqrtG6
#\"\"#\"\"\"-%$expG6#,$%#PiG#F)F(F)F/*&#F)F(F)*$F%F)F)!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "evalf(int(int(exp(x)*cos(y),y=0..Pi/4),x=0..Pi/2));" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{XPPMATH 20 "6#$\"+&R9Wp#!\"*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "This integral is approximately equ
al to 2.69." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 269 "" 0 "" {TEXT -1 
3 "14." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "int(int(cos(exp(x
*y)),y=0..2),x=0..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$,$*&
,&-%#CiG6#-%$expG6#,$%\"xG\"\"#!\"\"-F*6#\"\"\"F5F5F0F2F2/F0;\"\"!F1" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "evalf(int(int(cos(exp(x*y
)),y=0..2),x=0..2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+kGeHC!#5" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "This integral is approximately e
qual to -.24." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}{EXCHG {PARA 270 "" 0 "" {TEXT 
-1 3 "15." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(int(x^2*y,
x),y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%\"xG\"\"$\"\"\")%\"yG
\"\"#F(#F(\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%" }}}}{MARK "66 0 0" 45 }
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