{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 256 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }{TEXT 256 24 "Linear A lgebra Powertool" }}{PARA 256 "" 0 "" {TEXT -1 29 "Quick Gram-Schmidt \+ with Maple" }}{PARA 0 "" 0 "" {TEXT 257 26 "Worksheet by Russell Blyth " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(lin alg);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "After loading the linal g package, it is worthwhile to look at the help page for the GramSchmi dt command that Maple provides." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "?GramSchmidt" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 153 "To demon strate the command, I want to construct a series of 5 vectors in which the ith vector has a 1 in the first i positions and fills out with ze roes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "del := (x,y) -> p iecewise(x " 0 "" {MPLTEXT 1 0 34 "GramSchmidt ([seq(vec[k],k=1..5)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " GramSchmidt([seq(vec[6-k],k=1..5)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }