{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 259 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 260 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "Courie r" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } } {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 21 "Math 340 Midterm Exam" }}{PARA 256 "" 0 "" {TEXT -1 13 "O ct. 22, 2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "Sample solution" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 10 "Problem 1:" }{TEXT -1 13 " (25 points)" }}{PARA 0 "" 0 "" {TEXT -1 6 " Let " }{XPPEDIT 18 0 "F[0] = 0;" "6#/&%\"FG6#\"\"!F' " }{TEXT -1 4 ", " }{XPPEDIT 18 0 "F[1] = 1;" "6#/&%\"FG6#\"\"\"F'" }{TEXT -1 10 " and " }{XPPEDIT 18 0 "F[k] = F[k-1]+F[k-2];" "6#/& %\"FG6#%\"kG,&&F%6#,&F'\"\"\"F,!\"\"F,&F%6#,&F'F,\"\"#F-F," }{TEXT -1 6 " for " }{XPPEDIT 18 0 "k;" "6#%\"kG" }{TEXT -1 84 " = 2, 3, ... b e the Fibonacci numbers. It is known that the sequence of the ratio \+ " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "s[k] = F[k-1]/F[k];" "6#/&%\"sG6# %\"kG*&&%\"FG6#,&F'\"\"\"F-!\"\"F-&F*6#F'F." }{TEXT -1 10 ", for \+ " }{XPPEDIT 18 0 "k;" "6#%\"kG" }{TEXT -1 12 " = 1, 2, ..." }}{PARA 0 "" 0 "" {TEXT -1 87 "converges to the ration of golden section (0.618. ..). Write a program that, for input " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 30 ", output the entire sequence " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "s[1];" "6#&%\"sG6#\"\"\"" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "s[2];" "6#&%\"sG6#\"\"#" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "s[3]; " "6#&%\"sG6#\"\"$" }{TEXT -1 8 ", ..., " }{XPPEDIT 18 0 "s[n];" "6#& %\"sG6#%\"nG" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 265 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 257 "" 0 "" {TEXT -1 310 "fibratio := proc( n )\n local F, s, k;\n\n # construct the Fibonacci sequence\n F[0], F[1] := 0, 1 ;\n for k from 2 to n do\n F[k] := F[k-1] + F[k-2];\n end do; \n\n # construct the ratio sequence\n for k from 1 to n do\n \+ s[k] := evalf(F[k-1]/F[k]);\n end do;\n\n return seq(s[k],k=1..n); \nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "read \"e:/340/fib ratio.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "fibratio(10 );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6,$\"\"!F$$\"\"\"F$$\"+++++]!#5$\" +nmmmmF)$\"+++++gF)$\"++++]iF)$\"+ah%Q:'F)$\"+!>w/>'F)$\"+)eqk<'F)$\"+ #===='F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 10 "Problem 2:" }{TEXT -1 14 " (25 points)" }}{PARA 0 "" 0 "" {TEXT -1 44 "Write a program tha t, for an input vector " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT -1 4 " = [" }{XPPEDIT 18 0 "a[1];" "6#&%\"aG6#\"\"\"" }{TEXT -1 2 ", " } {XPPEDIT 18 0 "a[2];" "6#&%\"aG6#\"\"#" }{TEXT -1 6 ", ... " } {XPPEDIT 18 0 "a[n];" "6#&%\"aG6#%\"nG" }{TEXT -1 23 "], output the q uantity" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "S = sqrt(Sum((a[i]-mu)^2,i = 1 .. n))/(Sum(abs(a[i]),i = 1 .. n)*sqrt(Sum(a[i]^2,i = 1 .. n))); " "6#/%\"SG*&-%%sqrtG6#-%$SumG6$*$,&&%\"aG6#%\"iG\"\"\"%#muG!\"\"\"\"# /F1;F2%\"nGF2*&-F*6$-%$absG6#&F/6#F1/F1;F2F8F2-F'6#-F*6$*$&F/6#F1F5/F1 ;F2F8F2F4" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "where " } {XPPEDIT 18 0 "mu = Sum(a[i],i = 1 .. n)/n;" "6#/%#muG*&-%$SumG6$&%\"a G6#%\"iG/F,;\"\"\"%\"nGF/F0!\"\"" }{TEXT -1 74 ". Use a randomly ge nerated vector of dimension 10 to test your program." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 9 "Solution:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 428 "midtermp2 := pr oc( a )\n local mu, n, k, s1, s2, s3;\n\n n := LinearAlgebra[Dimen sion](a);\n \n # compute mu\n mu := 0;\n for k from 1 to n do \n mu := mu + a[k];\n end do;\n mu := evalf( mu/n );\n\n # \+ compute three sums\n s1, s2, s3 := 0, 0, 0;\n for k from 1 to n do \n s1 := s1 + (a[k]-mu)^2;\n s2 := s2 + abs(a[k]);\n s3 := s3 + a[k]^2;\n end do;\n\n return evalf( sqrt(s1)/(s2*sqrt(s3) ) );\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "read \"e:/340/midtermp2.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "a := LinearAlgebra[RandomVector][ro w](10,generator=-9..9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'RT ABLEG6%\"*sRwW\"-%'VECTORG6#7,!\"\"!\"$!\"%!\"'\"\"&F0F1!\")!\"&F-&%'V ectorG6#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "midtermp2 (a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+^qoy>!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 10 "Problem 3:" }{TEXT -1 12 " (25 points)" }}{PARA 0 " " 0 "" {TEXT -1 38 "For every pair of positive integers " }{XPPEDIT 18 0 "m;" "6#%\"mG" }{TEXT -1 9 " and " }{XPPEDIT 18 0 "n;" "6#%\" nG" }{TEXT -1 22 ", there are quotient " }{XPPEDIT 18 0 "q;" "6#%\"qG " }{TEXT -1 16 " and remainder " }{XPPEDIT 18 0 "r;" "6#%\"rG" } {TEXT -1 12 " such that " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "m = q*n+ r;" "6#/%\"mG,&*&%\"qG\"\"\"%\"nGF(F(%\"rGF(" }{TEXT -1 9 ", " }{XPPEDIT 18 0 "r < n;" "6#2%\"rG%\"nG" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "There is a simple method to compute " }{XPPEDIT 18 0 " q;" "6#%\"qG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "r;" "6#%\"rG" } {TEXT -1 4 ": " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 " Start with " }{XPPEDIT 18 0 "q = 0;" "6#/%\"qG\"\"! " }{TEXT -1 9 ", and " }{XPPEDIT 18 0 "r = m;" "6#/%\"rG%\"mG" } {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 " if " }{XPPEDIT 18 0 "r <= n;" "6#1%\"rG%\"nG" }{TEXT -1 9 ", then " }{XPPEDIT 18 0 "q = 0; " "6#/%\"qG\"\"!" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "r = m;" "6#/%\"r G%\"mG" }{TEXT -1 42 " is the solution, output result. Otherwise" }} {PARA 0 "" 0 "" {TEXT -1 16 " (*) increase " }{XPPEDIT 18 0 "q;" "6# %\"qG" }{TEXT -1 20 " by 1 and compute " }{XPPEDIT 18 0 "r = m-q*n; " "6#/%\"rG,&%\"mG\"\"\"*&%\"qGF'%\"nGF'!\"\"" }{TEXT -1 18 ", repea t until " }{XPPEDIT 18 0 "r < n;" "6#2%\"rG%\"nG" }{TEXT -1 11 " , o utput " }{XPPEDIT 18 0 "q;" "6#%\"qG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "r;" "6#%\"rG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 32 "Write a program that, for input " } {XPPEDIT 18 0 "m;" "6#%\"mG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "n;" " 6#%\"nG" }{TEXT -1 44 ", implement the above algorithm and output " } {XPPEDIT 18 0 "q;" "6#%\"qG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "r;" " 6#%\"rG" }{TEXT -1 17 " using while-do " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "For example: Let " }{XPPEDIT 18 0 "m = 38;" "6#/%\"mG\"#Q" }{TEXT -1 4 ", " }{XPPEDIT 18 0 "n = 9;" "6#/%\"nG\"\"*" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 3 " " } {XPPEDIT 18 0 "q = 0;" "6#/%\"qG\"\"!" }{TEXT -1 5 ", " }{XPPEDIT 18 0 "r = 38;" "6#/%\"rG\"#Q" }{TEXT -1 3 " > " }{XPPEDIT 18 0 "n;" "6 #%\"nG" }{TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 3 " " } {XPPEDIT 18 0 "q = 1;" "6#/%\"qG\"\"\"" }{TEXT -1 4 ", " }{XPPEDIT 18 0 "r = 38-1*9;" "6#/%\"rG,&\"#Q\"\"\"*&F'F'\"\"*F'!\"\"" }{TEXT -1 8 " = 31 > " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 11 " (repeat)" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "q = 2;" "6#/%\"qG\" \"#" }{TEXT -1 4 ", " }{XPPEDIT 18 0 "r = 38-2*9;" "6#/%\"rG,&\"#Q\" \"\"*&\"\"#F'\"\"*F'!\"\"" }{TEXT -1 8 " = 20 > " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 11 " (repeat)" }}{PARA 0 "" 0 "" {TEXT -1 3 " \+ " }{XPPEDIT 18 0 "q = 3;" "6#/%\"qG\"\"$" }{TEXT -1 4 ", " } {XPPEDIT 18 0 "r = 38-3*9;" "6#/%\"rG,&\"#Q\"\"\"*&\"\"$F'\"\"*F'!\"\" " }{TEXT -1 8 " = 11 > " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 11 " \+ (repeat)" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{XPPEDIT 18 0 "q = 4; " "6#/%\"qG\"\"%" }{TEXT -1 4 ", " }{XPPEDIT 18 0 "r = 38-4*9;" "6#/ %\"rG,&\"#Q\"\"\"*&\"\"%F'\"\"*F'!\"\"" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "2 < n;" "6#2\"\"#%\"nG" }{TEXT -1 20 " (end repeating)" }} {PARA 0 "" 0 "" {TEXT -1 12 "Therefore, " }{XPPEDIT 18 0 "q = 4;" "6# /%\"qG\"\"%" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "r = 2;" "6#/%\"rG\"\"# " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 267 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 " " 0 "" {TEXT -1 158 "quorem := proc( m, n )\n local q, r;\n\n q := 0; \n r := m;\n\n while r >= n do\n q := q + 1;\n r := m - q*n;\n end do;\n\n return q, r;\nend proc;" }}{PARA 0 "" 0 " " {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "read \"e:/340/quorem.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "q, r := quorem(38,9);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>6$%\"qG%\"rG6$\"\"%\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 10 "Problem 4:" }{TEXT -1 13 " (25 points)" }}{PARA 0 "" 0 "" {TEXT -1 76 "Many Fibonacci numbers are prime numbers. Write a program that , for input " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 32 ", find al l prime numbers among" }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "F[0];" "6#&% \"FG6#\"\"!" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "F[1];" "6#&%\"FG6#\"\" \"" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "F[2];" "6#&%\"FG6#\"\"#" }{TEXT -1 11 ", ..., " }{XPPEDIT 18 0 "F[n];" "6#&%\"FG6#%\"nG" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Output those prime numbers in a vector " }{XPPEDIT 18 0 "p;" "6#%\"pG" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 268 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 317 "fibprime := \+ proc(n)\n local F, u, k, c;\n\n F[0], F[1] := 0, 1;\n for k from 2 to n do\n F[k] := F[k-1] + F[k-2];\n end do;\n\n u := Vect or[row](n);\n c := 0;\n for k from 1 to n do\n if isprime(F[k ]) then\n c := c + 1;\n u[c] := F[k];\n end if;\n end do;\n\n return u[1..c];\nend proc;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "read \"e:/340/fib prime.txt\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "fibprime(40 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*K^wW\"-%'VECTORG6 #7+\"\"#\"\"$\"\"&\"#8\"#*)\"$L#\"%(f\"\"&d'G\"'HU^&%'VectorG6#%$rowG " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 13 "Problem 5: " }{TEXT -1 17 "(Extra 15 points)" }} {PARA 0 "" 0 "" {TEXT -1 45 "Write a program that, for an input vecto r " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT -1 4 " = [" }{XPPEDIT 18 0 "a[1];" "6#&%\"aG6#\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "a[2];" "6# &%\"aG6#\"\"#" }{TEXT -1 6 ", ... " }{XPPEDIT 18 0 "a[n];" "6#&%\"aG6# %\"nG" }{TEXT -1 25 "], output two vectors " }{XPPEDIT 18 0 "u;" "6 #%\"uG" }{TEXT -1 7 " and " }{XPPEDIT 18 0 "v;" "6#%\"vG" }{TEXT -1 83 " containing the positive entries and negative entries respectivel y. For example:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 269 9 "Solution:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 " " 0 "" {TEXT -1 376 "vecsplit := proc( a )\n local n, u, v, c, d, k; \n\n n := LinearAlgebra[Dimension](a);\n u := Vector[row](n);\n \+ v := Vector[row](n);\n\n c, d := 0, 0;\n for k from 1 to n do\n \+ if a[k] > 0 then\n c := c + 1;\n u[c] := a[k];\n \+ elif a[k] < 0 then\n d := d + 1;\n v[d] := a[k];\n \+ end if;\n end do;\n\n return u[1..c], v[1..d];\nend proc;" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "read \"e:/340/vecsplit.txt\":" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "a := LinearAlgebra[RandomVector][row](10,generator =-5..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG-%'RTABLEG6%\"*s`wW \"-%'VECTORG6#7,!\"&\"\"\"\"\"&!\"$\"\"$!\"#F/!\"\"F0\"\"#&%'VectorG6# %$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "u, v := vecsplit( a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"uG%\"vG6$-%'RTABLEG6%\"*# \\lZ9-%'VECTORG6#7'\"\"\"\"\"&\"\"$F1\"\"#&%'VectorG6#%$rowG-F)6%\"*Kb wW\"-F-6#7'!\"&!\"$!\"#!\"\"F?F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "1 8 6 0" 135 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 144763972 144765132 144765372 144765492 144765532 } {RTABLE M7R0 I6RTABLE_SAVE/144763972X*%)anythingG6"6"[gl!$%!!!"+"+!""!"$!"%!"'""&F*F+!")!"&F 'F& } {RTABLE M7R0 I6RTABLE_SAVE/144765132X*%)anythingG6"6"[gl!$%!!!"*"*""#""$""&"#8"#*)"$L#"%(f"" &d'G"'HU^F& } {RTABLE M7R0 I6RTABLE_SAVE/144765372X*%)anythingG6"6"[gl!$%!!!"+"+!"&"""""&!"$""$!"#F)!""F*" "#F& } {RTABLE M7R0 I6RTABLE_SAVE/144765492X*%)anythingG6"6"[gl!$%!!!"&"&"""""&""$F(""#F& } {RTABLE M7R0 I6RTABLE_SAVE/144765532X*%)anythingG6"6"[gl!$%!!!"&"&!"&!"$!"#!""F(F& }