This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2019.3.28)  9 FEB 2021 20:55
entering extended mode
 \write18 enabled.
 file:line:error style messages enabled.
 %&-line parsing enabled.
**questions-project1.tex
(./questions-project1.tex
LaTeX2e <2018-04-01> patch level 2
Babel <3.18> and hyphenation patterns for 84 language(s) loaded.
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/size12.clo
File: size12.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
)
\c@part=\count80
\c@section=\count81
\c@subsection=\count82
\c@subsubsection=\count83
\c@paragraph=\count84
\c@subparagraph=\count85
\c@figure=\count86
\c@table=\count87
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/amsmath/amsmath.sty
Package: amsmath 2017/09/02 v2.17a AMS math features
\@mathmargin=\skip43

For additional information on amsmath, use the `?' option.
(/usr/local/texlive/2018/texmf-dist/tex/latex/amsmath/amstext.sty
Package: amstext 2000/06/29 v2.01 AMS text

(/usr/local/texlive/2018/texmf-dist/tex/latex/amsmath/amsgen.sty
File: amsgen.sty 1999/11/30 v2.0 generic functions
\@emptytoks=\toks14
\ex@=\dimen103
))
(/usr/local/texlive/2018/texmf-dist/tex/latex/amsmath/amsbsy.sty
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
\pmbraise@=\dimen104
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/amsmath/amsopn.sty
Package: amsopn 2016/03/08 v2.02 operator names
)
\inf@bad=\count88
LaTeX Info: Redefining \frac on input line 213.
\uproot@=\count89
\leftroot@=\count90
LaTeX Info: Redefining \overline on input line 375.
\classnum@=\count91
\DOTSCASE@=\count92
LaTeX Info: Redefining \ldots on input line 472.
LaTeX Info: Redefining \dots on input line 475.
LaTeX Info: Redefining \cdots on input line 596.
\Mathstrutbox@=\box26
\strutbox@=\box27
\big@size=\dimen105
LaTeX Font Info:    Redeclaring font encoding OML on input line 712.
LaTeX Font Info:    Redeclaring font encoding OMS on input line 713.
\macc@depth=\count93
\c@MaxMatrixCols=\count94
\dotsspace@=\muskip10
\c@parentequation=\count95
\dspbrk@lvl=\count96
\tag@help=\toks15
\row@=\count97
\column@=\count98
\maxfields@=\count99
\andhelp@=\toks16
\eqnshift@=\dimen106
\alignsep@=\dimen107
\tagshift@=\dimen108
\tagwidth@=\dimen109
\totwidth@=\dimen110
\lineht@=\dimen111
\@envbody=\toks17
\multlinegap=\skip44
\multlinetaggap=\skip45
\mathdisplay@stack=\toks18
LaTeX Info: Redefining \[ on input line 2817.
LaTeX Info: Redefining \] on input line 2818.
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/amscls/amsthm.sty
Package: amsthm 2017/10/31 v2.20.4
\thm@style=\toks19
\thm@bodyfont=\toks20
\thm@headfont=\toks21
\thm@notefont=\toks22
\thm@headpunct=\toks23
\thm@preskip=\skip46
\thm@postskip=\skip47
\thm@headsep=\skip48
\dth@everypar=\toks24
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2013/01/14 v3.01 AMS font symbols

(/usr/local/texlive/2018/texmf-dist/tex/latex/amsfonts/amsfonts.sty
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
\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 106.
))
(/usr/local/texlive/2018/texmf-dist/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 52.
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/enumitem/enumitem.sty
Package: enumitem 2011/09/28 v3.5.2 Customized lists
\enitkv@toks@=\toks25
\labelindent=\skip49
\enit@outerparindent=\dimen112
\enit@toks=\toks26
\enit@inbox=\box28
\enitdp@description=\count100
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/hyperref/hyperref.sty
Package: hyperref 2018/02/06 v6.86b Hypertext links for LaTeX

(/usr/local/texlive/2018/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty
Package: hobsub-hyperref 2016/05/16 v1.14 Bundle oberdiek, subset hyperref (HO)


(/usr/local/texlive/2018/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty
Package: hobsub-generic 2016/05/16 v1.14 Bundle oberdiek, subset generic (HO)
Package: hobsub 2016/05/16 v1.14 Construct package bundles (HO)
Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO)
Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO)
Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO)
Package ifluatex Info: LuaTeX not detected.
Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO)
Package ifvtex Info: VTeX not detected.
Package: intcalc 2016/05/16 v1.2 Expandable calculations with integers (HO)
Package: ifpdf 2017/03/15 v3.2 Provides the ifpdf switch
Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO)
Package etexcmds Info: Could not find \expanded.
(etexcmds)             That can mean that you are not using pdfTeX 1.50 or
(etexcmds)             that some package has redefined \expanded.
(etexcmds)             In the latter case, load this package earlier.
Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO)
Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO)
Package: pdftexcmds 2018/01/30 v0.27 Utility functions of pdfTeX for LuaTeX (HO
)
Package pdftexcmds Info: LuaTeX not detected.
Package pdftexcmds Info: \pdf@primitive is available.
Package pdftexcmds Info: \pdf@ifprimitive is available.
Package pdftexcmds Info: \pdfdraftmode found.
Package: pdfescape 2016/05/16 v1.14 Implements pdfTeX's escape features (HO)
Package: bigintcalc 2016/05/16 v1.4 Expandable calculations on big integers (HO
)
Package: bitset 2016/05/16 v1.2 Handle bit-vector datatype (HO)
Package: uniquecounter 2016/05/16 v1.3 Provide unlimited unique counter (HO)
)
Package hobsub Info: Skipping package `hobsub' (already loaded).
Package: letltxmacro 2016/05/16 v1.5 Let assignment for LaTeX macros (HO)
Package: hopatch 2016/05/16 v1.3 Wrapper for package hooks (HO)
Package: xcolor-patch 2016/05/16 xcolor patch
Package: atveryend 2016/05/16 v1.9 Hooks at the very end of document (HO)
Package atveryend Info: \enddocument detected (standard20110627).
Package: atbegshi 2016/06/09 v1.18 At begin shipout hook (HO)
Package: refcount 2016/05/16 v3.5 Data extraction from label references (HO)
Package: hycolor 2016/05/16 v1.8 Color options for hyperref/bookmark (HO)
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics/keyval.sty
Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
\KV@toks@=\toks27
)
(/usr/local/texlive/2018/texmf-dist/tex/generic/ifxetex/ifxetex.sty
Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/oberdiek/auxhook.sty
Package: auxhook 2016/05/16 v1.4 Hooks for auxiliary files (HO)
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/oberdiek/kvoptions.sty
Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO)
)
\@linkdim=\dimen113
\Hy@linkcounter=\count101
\Hy@pagecounter=\count102

(/usr/local/texlive/2018/texmf-dist/tex/latex/hyperref/pd1enc.def
File: pd1enc.def 2018/02/06 v6.86b Hyperref: PDFDocEncoding definition (HO)
Now handling font encoding PD1 ...
... no UTF-8 mapping file for font encoding PD1
)
\Hy@SavedSpaceFactor=\count103

(/usr/local/texlive/2018/texmf-dist/tex/latex/latexconfig/hyperref.cfg
File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
)
Package hyperref Info: Hyper figures OFF on input line 4509.
Package hyperref Info: Link nesting OFF on input line 4514.
Package hyperref Info: Hyper index ON on input line 4517.
Package hyperref Info: Plain pages OFF on input line 4524.
Package hyperref Info: Backreferencing OFF on input line 4529.
Package hyperref Info: Implicit mode ON; LaTeX internals redefined.
Package hyperref Info: Bookmarks ON on input line 4762.
\c@Hy@tempcnt=\count104

(/usr/local/texlive/2018/texmf-dist/tex/latex/url/url.sty
\Urlmuskip=\muskip11
Package: url 2013/09/16  ver 3.4  Verb mode for urls, etc.
)
LaTeX Info: Redefining \url on input line 5115.
\XeTeXLinkMargin=\dimen114
\Fld@menulength=\count105
\Field@Width=\dimen115
\Fld@charsize=\dimen116
Package hyperref Info: Hyper figures OFF on input line 6369.
Package hyperref Info: Link nesting OFF on input line 6374.
Package hyperref Info: Hyper index ON on input line 6377.
Package hyperref Info: backreferencing OFF on input line 6384.
Package hyperref Info: Link coloring OFF on input line 6389.
Package hyperref Info: Link coloring with OCG OFF on input line 6394.
Package hyperref Info: PDF/A mode OFF on input line 6399.
LaTeX Info: Redefining \ref on input line 6439.
LaTeX Info: Redefining \pageref on input line 6443.
\Hy@abspage=\count106
\c@Item=\count107
\c@Hfootnote=\count108
)
Package hyperref Info: Driver (autodetected): hpdftex.

(/usr/local/texlive/2018/texmf-dist/tex/latex/hyperref/hpdftex.def
File: hpdftex.def 2018/02/06 v6.86b Hyperref driver for pdfTeX
\Fld@listcount=\count109
\c@bookmark@seq@number=\count110

(/usr/local/texlive/2018/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty
Package: rerunfilecheck 2016/05/16 v1.8 Rerun checks for auxiliary files (HO)
Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2
82.
)
\Hy@SectionHShift=\skip50
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/geometry/geometry.sty
Package: geometry 2018/03/24 v5.7 Page Geometry
\Gm@cnth=\count111
\Gm@cntv=\count112
\c@Gm@tempcnt=\count113
\Gm@bindingoffset=\dimen117
\Gm@wd@mp=\dimen118
\Gm@odd@mp=\dimen119
\Gm@even@mp=\dimen120
\Gm@layoutwidth=\dimen121
\Gm@layoutheight=\dimen122
\Gm@layouthoffset=\dimen123
\Gm@layoutvoffset=\dimen124
\Gm@dimlist=\toks28
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/appendix/appendix.sty
Package: appendix 2009/09/02 v1.2b extra appendix facilities
\c@@pps=\count114
\c@@ppsavesec=\count115
\c@@ppsaveapp=\count116
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics/graphics.sty
Package: graphics 2017/06/25 v1.2c Standard LaTeX Graphics (DPC,SPQR)

(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics/trig.sty
Package: trig 2016/01/03 v1.10 sin cos tan (DPC)
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
)
Package graphics Info: Driver file: pdftex.def on input line 99.

(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics-def/pdftex.def
File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex
))
(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/babel.sty
Package: babel 2018/02/14 3.18 The Babel package

(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/switch.def
File: switch.def 2018/02/14 3.18 Babel switching mechanism
)
(/usr/local/texlive/2018/texmf-dist/tex/generic/babel-english/english.ldf
Language: english 2017/06/06 v3.3r English support from the babel system

(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/babel.def
File: babel.def 2018/02/14 3.18 Babel common definitions
\babel@savecnt=\count117
\U@D=\dimen125

(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/txtbabel.def)
\bbl@dirlevel=\count118
)
\l@canadian = a dialect from \language\l@american 
\l@australian = a dialect from \language\l@british 
\l@newzealand = a dialect from \language\l@british 
))
(/usr/local/texlive/2018/texmf-dist/tex/latex/tools/multicol.sty
Package: multicol 2018/04/01 v1.8r multicolumn formatting (FMi)
\c@tracingmulticols=\count119
\mult@box=\box29
\multicol@leftmargin=\dimen126
\c@unbalance=\count120
\c@collectmore=\count121
\doublecol@number=\count122
\multicoltolerance=\count123
\multicolpretolerance=\count124
\full@width=\dimen127
\page@free=\dimen128
\premulticols=\dimen129
\postmulticols=\dimen130
\multicolsep=\skip51
\multicolbaselineskip=\skip52
\partial@page=\box30
\last@line=\box31
\maxbalancingoverflow=\dimen131
\mult@rightbox=\box32
\mult@grightbox=\box33
\mult@gfirstbox=\box34
\mult@firstbox=\box35
\@tempa=\box36
\@tempa=\box37
\@tempa=\box38
\@tempa=\box39
\@tempa=\box40
\@tempa=\box41
\@tempa=\box42
\@tempa=\box43
\@tempa=\box44
\@tempa=\box45
\@tempa=\box46
\@tempa=\box47
\@tempa=\box48
\@tempa=\box49
\@tempa=\box50
\@tempa=\box51
\@tempa=\box52
\c@columnbadness=\count125
\c@finalcolumnbadness=\count126
\last@try=\dimen132
\multicolovershoot=\dimen133
\multicolundershoot=\dimen134
\mult@nat@firstbox=\box53
\colbreak@box=\box54
\mc@col@check@num=\count127
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/psnfss/times.sty
Package: times 2005/04/12 PSNFSS-v9.2a (SPQR) 
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/fontenc.sty
Package: fontenc 2017/04/05 v2.0i Standard LaTeX package

(/usr/local/texlive/2018/texmf-dist/tex/latex/base/t1enc.def
File: t1enc.def 2017/04/05 v2.0i Standard LaTeX file
LaTeX Font Info:    Redeclaring font encoding T1 on input line 48.
))
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/inputenc.sty
Package: inputenc 2018/04/06 v1.3b Input encoding file
\inpenc@prehook=\toks29
\inpenc@posthook=\toks30
)
(/usr/local/texlive/2018/texmf-dist/tex/latex/xcolor/xcolor.sty
Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK)

(/usr/local/texlive/2018/texmf-dist/tex/latex/graphics-cfg/color.cfg
File: color.cfg 2016/01/02 v1.6 sample color configuration
)
Package xcolor Info: Driver file: pdftex.def on input line 225.
Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348.
Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352.
Package xcolor Info: Model `RGB' extended on input line 1364.
Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366.
Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367.
Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368.
Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369.
Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370.
Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371.
)
\c@rem=\count128
\c@exm=\count129
\c@exercise=\count130
\c@exms=\count131
\c@prp=\count132
\c@thm=\count133
\c@lemma=\count134
\c@question=\count135
\c@ans=\count136
\c@wans=\count137

(./questions-project1.aux)
\openout1 = `questions-project1.aux'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Checking defaults for PD1/pdf/m/n on input line 120.
LaTeX Font Info:    ... okay on input line 120.
LaTeX Font Info:    Try loading font information for T1+ptm on input line 120.

(/usr/local/texlive/2018/texmf-dist/tex/latex/psnfss/t1ptm.fd
File: t1ptm.fd 2001/06/04 font definitions for T1/ptm.
)
\AtBeginShipoutBox=\box55
Package hyperref Info: Link coloring OFF on input line 120.

(/usr/local/texlive/2018/texmf-dist/tex/latex/hyperref/nameref.sty
Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section

(/usr/local/texlive/2018/texmf-dist/tex/generic/oberdiek/gettitlestring.sty
Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO)
)
\c@section@level=\count138
)
LaTeX Info: Redefining \ref on input line 120.
LaTeX Info: Redefining \pageref on input line 120.
LaTeX Info: Redefining \nameref on input line 120.

(./questions-project1.out) (./questions-project1.out)
\@outlinefile=\write3
\openout3 = `questions-project1.out'.


*geometry* driver: auto-detecting
*geometry* detected driver: pdftex
*geometry* verbose mode - [ preamble ] result:
* driver: pdftex
* paper: <default>
* layout: <same size as paper>
* layoutoffset:(h,v)=(0.0pt,0.0pt)
* modes: landscape 
* h-part:(L,W,R)=(85.35826pt, 595.8007pt, 113.81102pt)
* v-part:(T,H,B)=(56.9055pt, 500.484pt, 56.9055pt)
* \paperwidth=794.96999pt
* \paperheight=614.295pt
* \textwidth=595.8007pt
* \textheight=500.484pt
* \oddsidemargin=13.08827pt
* \evensidemargin=13.08827pt
* \topmargin=-52.36449pt
* \headheight=12.0pt
* \headsep=25.0pt
* \topskip=12.0pt
* \footskip=30.0pt
* \marginparwidth=113.81102pt
* \marginparsep=10.0pt
* \columnsep=10.0pt
* \skip\footins=10.8pt plus 4.0pt minus 2.0pt
* \hoffset=0.0pt
* \voffset=0.0pt
* \mag=1000
* \@twocolumnfalse
* \@twosidefalse
* \@mparswitchfalse
* \@reversemarginfalse
* (1in=72.27pt=25.4mm, 1cm=28.453pt)

(/usr/local/texlive/2018/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
[Loading MPS to PDF converter (version 2006.09.02).]
\scratchcounter=\count139
\scratchdimen=\dimen135
\scratchbox=\box56
\nofMPsegments=\count140
\nofMParguments=\count141
\everyMPshowfont=\toks31
\MPscratchCnt=\count142
\MPscratchDim=\dimen136
\MPnumerator=\count143
\makeMPintoPDFobject=\count144
\everyMPtoPDFconversion=\toks32
) (/usr/local/texlive/2018/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
Package: epstopdf-base 2016/05/15 v2.6 Base part for package epstopdf

(/usr/local/texlive/2018/texmf-dist/tex/latex/oberdiek/grfext.sty
Package: grfext 2016/05/16 v1.2 Manage graphics extensions (HO)
)
Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
38.
Package grfext Info: Graphics extension search list:
(grfext)             [.pdf,.png,.jpg,.mps,.jpeg,.jbig2,.jb2,.PDF,.PNG,.JPG,.JPE
G,.JBIG2,.JB2,.eps]
(grfext)             \AppendGraphicsExtensions on input line 456.

(/usr/local/texlive/2018/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
e
))
LaTeX Font Info:    Font shape `T1/ptm/bx/n' in size <17.28> not available
(Font)              Font shape `T1/ptm/b/n' tried instead on input line 149.
LaTeX Font Info:    Font shape `T1/ptm/bx/n' in size <12> not available
(Font)              Font shape `T1/ptm/b/n' tried instead on input line 153.
LaTeX Font Info:    Try loading font information for U+msa on input line 158.

(/usr/local/texlive/2018/texmf-dist/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
)
LaTeX Font Info:    Try loading font information for U+msb on input line 158.

(/usr/local/texlive/2018/texmf-dist/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
)
LaTeX Font Info:    Try loading font information for U+lasy on input line 158.

(/usr/local/texlive/2018/texmf-dist/tex/latex/base/ulasy.fd
File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions
) [1

{/usr/local/texlive/2018/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
LaTeX Font Info:    Try loading font information for OMS+ptm on input line 181.


(/usr/local/texlive/2018/texmf-dist/tex/latex/psnfss/omsptm.fd
File: omsptm.fd 
)
LaTeX Font Info:    Font shape `OMS/ptm/m/n' in size <12> not available
(Font)              Font shape `OMS/cmsy/m/n' tried instead on input line 181.
LaTeX Font Info:    Try loading font information for T1+pcr on input line 184.

(/usr/local/texlive/2018/texmf-dist/tex/latex/psnfss/t1pcr.fd
File: t1pcr.fd 2001/06/04 font definitions for T1/pcr.
)pdfTeX warning (ext4): destination with the same identifier (name{page.i}) has
 been already used, duplicate ignored
<to be read again> 
                   \relax 
l.254 $$
        A_0= \left( \begin{array}{ccc} [1]
Package atveryend Info: Empty hook `BeforeClearDocument' on input line 310.
 [2]
Package atveryend Info: Empty hook `AfterLastShipout' on input line 310.
 (./questions-project1.aux)
Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 310.
Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 310.
Package rerunfilecheck Info: File `questions-project1.out' has not changed.
(rerunfilecheck)             Checksum: D41D8CD98F00B204E9800998ECF8427E;0.
Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 310.
 ) 
Here is how much of TeX's memory you used:
 8115 strings out of 492649
 114412 string characters out of 6129622
 229108 words of memory out of 5000000
 11864 multiletter control sequences out of 15000+600000
 22808 words of font info for 47 fonts, out of 8000000 for 9000
 1141 hyphenation exceptions out of 8191
 28i,7n,35p,259b,464s stack positions out of 5000i,500n,10000p,200000b,80000s
{/usr/local/texlive/2018/texmf-dist/fonts/enc/dvips/base/8r.enc}</usr/local/t
exlive/2018/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/local/te
xlive/2018/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi12.pfb></usr/local/tex
live/2018/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi8.pfb></usr/local/texli
ve/2018/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr/local/texlive
/2018/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive/20
18/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/texlive/201
8/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/local/texlive/2018/
texmf-dist/fonts/type1/urw/courier/ucrr8a.pfb></usr/local/texlive/2018/texmf-di
st/fonts/type1/urw/times/utmb8a.pfb></usr/local/texlive/2018/texmf-dist/fonts/t
ype1/urw/times/utmr8a.pfb></usr/local/texlive/2018/texmf-dist/fonts/type1/urw/t
imes/utmri8a.pfb>
Output written on questions-project1.pdf (3 pages, 115742 bytes).
PDF statistics:
 82 PDF objects out of 1000 (max. 8388607)
 65 compressed objects within 1 object stream
 16 named destinations out of 1000 (max. 500000)
 1 words of extra memory for PDF output out of 10000 (max. 10000000)

