This is pdfTeX, Version 3.1415926-1.40.9 (MiKTeX 2.7) (preloaded format=pdflatex 2008.12.3) 25 SEP 2009 14:44 entering extended mode **review1_sol_09.tex (review1_sol_09.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, dumylang, nohyphenation, ge rman, ngerman, german-x-2008-06-18, ngerman-x-2008-06-18, french, loaded. ("C:\Program Files\MiKTeX 2.7\tex\latex\base\article.cls" Document Class: article 2005/09/16 v1.4f Standard LaTeX document class ("C:\Program Files\MiKTeX 2.7\tex\latex\base\size12.clo" File: size12.clo 2005/09/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) ("C:\Program Files\MiKTeX 2.7\tex\latex\amsfonts\amssymb.sty" Package: amssymb 2002/01/22 v2.2d ("C:\Program Files\MiKTeX 2.7\tex\latex\amsfonts\amsfonts.sty" Package: amsfonts 2001/10/25 v2.2f \@emptytoks=\toks14 \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. )) ("C:\Program Files\MiKTeX 2.7\tex\latex\base\latexsym.sty" Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols) \symlasy=\mathgroup6 LaTeX Font Info: Overwriting symbol font `lasy' in version `bold' (Font) U/lasy/m/n --> U/lasy/b/n on input line 47. ) ("C:\Program Files\MiKTeX 2.7\tex\latex\amsmath\amsmath.sty" Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. 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("C:\Program Files\MiKTeX 2.7\tex\latex\base\ulasy.fd" File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions ) Overfull \hbox (79.08627pt too wide) in paragraph at lines 24--41 []\OT1/cmr/m/n/12 Show that $\OML/cmm/m/it/12 A \OT1/cmr/m/n/12 = []$ is row eq uiv-a-lent to $[]$. [] Overfull \hbox (94.08067pt too wide) in paragraph at lines 24--41 \OT1/cmr/m/n/12 Solution: $\OML/cmm/m/it/12 A \OT1/cmr/m/n/12 = []$ $\OMS/cmsy/ m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 := \OML/cmm/m /it/12 r[] \OT1/cmr/m/n/12 + 2\OML/cmm/m/it/12 r[]$\OT1/cmr/m/n/12 ) $[]$ [] [1 {C:/Documents and Settings/All Users/Application Data/MiKTeX/2.7/pdftex/config/ pdftex.map}] Overfull \hbox (19.10275pt too wide) in paragraph at lines 66--85 \OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 := \OML/cmm/m/it/12 r[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 r[]$\OT1/cmr/m/n/12 ) $[]$ $\OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n /12 := \OML/cmm/m/it/12 r[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 r[]$\OT1/cmr/m/ n/12 ) $[]$ [] Overfull \hbox (41.97748pt too wide) in paragraph at lines 66--85 \OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 := \OML/cmm/m/it/12 r[] \OMS/cmsy/m/n/12 \OML/cmm/m/it/12 r[]$\OT1/cmr/m/n/12 ) $[]$$\OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n/ 12 := \OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 + 3\OML/cmm/m/it/12 r[]$\OT1/cmr/m/n /12 ) $[]$. [] [2] Overfull \hbox (75.04916pt too wide) in paragraph at lines 99--104 []$[]$ $[]$ $[]$ [] [3] [4] Overfull \hbox (19.13243pt too wide) in paragraph at lines 178--204 []$[]$ $\OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/ n/12 := \OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 + 2\OML/cmm/m/it/12 r[]$\OT1/cmr/m /n/12 ) $[]$ [] Overfull \hbox (76.17892pt too wide) in paragraph at lines 178--204 []$ $\OMS/cmsy/m/n/12 $ \OT1/cmr/m/n/12 ($\OML/cmm/m/it/12 r[] \OT1/cmr/m/n/1 2 := \OML/cmm/m/it/12 r[] \OT1/cmr/m/n/12 + 2\OML/cmm/m/it/12 r[]$\OT1/cmr/m/n/ 12 ) $[]$ [] [5] [6] Underfull \hbox (badness 10000) in paragraph at lines 237--245 [] [7] Package amsmath Warning: Cannot use `split' here; (amsmath) trying to recover with `aligned' on input line 306. [8] Package amsmath Warning: Cannot use `split' here; (amsmath) trying to recover with `aligned' on input line 355. Overfull \hbox (65.3111pt too wide) in alignment at lines 343--356 [][][] [] [] Package amsmath Warning: Cannot use `split' here; (amsmath) trying to recover with `aligned' on input line 386. Overfull \hbox (15.88258pt too wide) in alignment at lines 366--387 [][][] [] [] [9] [10] (review1_sol_09.aux) ) Here is how much of TeX's memory you used: 1190 strings out of 95304 12810 string characters out of 1183032 76758 words of memory out of 1500000 4413 multiletter control sequences out of 110000 8919 words of font info for 36 fonts, out of 3000000 for 5000 14 hyphenation exceptions out of 8191 27i,19n,24p,402b,347s stack positions out of 5000i,500n,10000p,200000b,50000s < C:/Program Files/MiKTeX 2.7/fonts/type1/bluesky/cm/cmmi12.pfb> Output written on review1_sol_09.pdf (10 pages, 64304 bytes). PDF statistics: 71 PDF objects out of 1000 (max. 8388607) 0 named destinations out of 1000 (max. 131072) 1 words of extra memory for PDF output out of 10000 (max. 10000000)