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{PSTYLE "Bullet Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 }0 0 0 -1 3 3 0 0 0 0 0 0 15 2 }{PSTYLE "Title" 0 18 1 
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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 18 "Matriisit maplessa" }}
{PARA 19 "" 0 "" {TEXT -1 8 "9.9.1998" }}{PARA 19 "" 0 "" {TEXT 256 
27 "K\344ynnistys UNIX-ty\366asemissa" }}{PARA 15 "" 0 "" {TEXT 257 9 
"use maple" }}{PARA 15 "" 0 "" {TEXT 258 7 "xmaple&" }}}{SECT 0 {PARA 
3 "" 0 "" {TEXT -1 35 "Matriisien k\344sittely, with(linalg):" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "restart:with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new
 definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new defi
nition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A:=matr
ix(3,4,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7%7&-%
\"aG6$\"\"\"F--F+6$F-\"\"#-F+6$F-\"\"$-F+6$F-\"\"%7&-F+6$F0F--F+6$F0F0
-F+6$F0F3-F+6$F0F67&-F+6$F3F--F+6$F3F0-F+6$F3F3-F+6$F3F6" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "B:=matrix(4,5,b);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7&7'-%\"bG6$\"\"\"F--F+6$F-\"\"#-F
+6$F-\"\"$-F+6$F-\"\"%-F+6$F-\"\"&7'-F+6$F0F--F+6$F0F0-F+6$F0F3-F+6$F0
F6-F+6$F0F97'-F+6$F3F--F+6$F3F0-F+6$F3F3-F+6$F3F6-F+6$F3F97'-F+6$F6F--
F+6$F6F0-F+6$F6F3-F+6$F6F6-F+6$F6F9" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "C:=evalm(A&*B):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "C[1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&-%\"aG6
$\"\"\"F(F(-%\"bGF'F(F(*&-F&6$F(\"\"#F(-F*6$F.F(F(F(*&-F&6$F(\"\"$F(-F
*6$F4F(F(F(*&-F&6$F(\"\"%F(-F*6$F:F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "evalm(B&*A);" }}{PARA 8 "" 1 "" {TEXT -1 78 "Error, (
in linalg[multiply]) non matching dimensions for vector/matrix product
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Eiv\344t kertomiskelpoisia j
\344rjestyksess\344 BA." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
AT:=transpose(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ATG-%'matrixG6
#7&7%-%\"aG6$\"\"\"F--F+6$\"\"#F--F+6$\"\"$F-7%-F+6$F-F0-F+6$F0F0-F+6$
F3F07%-F+6$F-F3-F+6$F0F3-F+6$F3F37%-F+6$F-\"\"%-F+6$F0FE-F+6$F3FE" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "BT:=transpose(B);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#BTG-%'matrixG6#7'7&-%\"bG6$\"\"\"F--F+6$
\"\"#F--F+6$\"\"$F--F+6$\"\"%F-7&-F+6$F-F0-F+6$F0F0-F+6$F3F0-F+6$F6F07
&-F+6$F-F3-F+6$F0F3-F+6$F3F3-F+6$F6F37&-F+6$F-F6-F+6$F0F6-F+6$F3F6-F+6
$F6F67&-F+6$F-\"\"&-F+6$F0FU-F+6$F3FU-F+6$F6FU" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 30 "evalm(transpose(A&*B)-BT&*AT);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'matrixG6#7'7%\"\"!F(F(F'F'F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 19 "Gaussin eliminaatio" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" 
{TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 110 "Ab:=matrix(4,4,[1,-1,1,0,\n                -1
,1,-1,0,\n                20,10,0,80,\n                0,10,25,90]);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AbG-%'matrixG6#7&7&\"\"\"!\"\"F*
\"\"!7&F+F*F+F,7&\"#?\"#5F,\"#!)7&F,F0\"#D\"#!*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "Ab1:=addrow(Ab,1,2,1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$Ab1G-%'matrixG6#7&7&\"\"\"!\"\"F*\"\"!7&F,F,F,F,7&\"
#?\"#5F,\"#!)7&F,F0\"#D\"#!*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "M
ik\344 rivi lis\344t\344\344n mihin ja mill\344 kerrotaan (siis ensin \+
mainittu)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "Ab2:=addrow(Ab1,1,3,-20);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$Ab2G-%'matrixG6#7&7&\"\"\"!\"\"F*\"\"!7&F,F,F,F,7&F,
\"#I!#?\"#!)7&F,\"#5\"#D\"#!*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "
Saatiin 1. sarake nollatuksi. Toinen on 0-rivi, pudotetaan se pohjalle
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Ab3:=swaprow(Ab2,2,4);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Ab3G-%'matrixG6#7&7&\"\"\"!\"\"
F*\"\"!7&F,\"#5\"#D\"#!*7&F,\"#I!#?\"#!)7&F,F,F,F," }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 24 "Ab4:=addrow(Ab3,2,3,-3);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$Ab4G-%'matrixG6#7&7&\"\"\"!\"\"F*\"\"!7&F,\"#5\"#D
\"#!*7&F,F,!#&*!$!>7&F,F,F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "
Eliminaatiovaihe on valmis. Suoritetaan takaisinsijoitus." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "x3:=solve(-95*x=-190,x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#x3G\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "x2:=solve(10*x2+25*x3=90,x2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#x2G\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "x1:=solve(x1-x2+x3=0,x1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x1
G\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Tarkistetaanpa viel\344
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "A:=submatrix(Ab,1..4,1
..3);b:=col(Ab,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG
6#7&7%\"\"\"!\"\"F*7%F+F*F+7%\"#?\"#5\"\"!7%F0F/\"#D" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"bG-%'vectorG6#7&\"\"!F)\"#!)\"#!*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "evalm(A&*vector([x1,x2,x3]));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&\"\"!F'\"#!)\"#!*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Kyll\344 vaan !" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "3" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }