This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 23:28 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **Q17.tex (./Q17.tex LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-01-22> ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1 \textbf{Question 17} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 []\OT1/cmr/bx/n/10 Question [] Overfull \hbox (11.49994pt too wide) in paragraph at lines 1--2 \OT1/cmr/bx/n/10 17 [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3 À partir des huit pôles obtenus avec la commande par retour d'état de... You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. LaTeX Font Info: Trying to load font information for +cmr on input line 3. LaTeX Font Info: No file cmr.fd. on input line 3. LaTeX Font Warning: Font shape `/cmr/m/n' undefined (Font) using `/cmr/m/n' instead on input line 3. ! Corrupted NFSS tables. wrong@fontshape ...message {Corrupted NFSS tables} error@fontshape else let f... l.3 À partir des huit pôles obtenus avec la commande par retour d'état de... This error message was generated by an \errmessage command, so I can't give any explicit help. Pretend that you're Hercule Poirot: Examine all clues, and deduce the truth by order and method. LaTeX Font Warning: Font shape `/cmr/m/n' undefined (Font) using `OT1/cmr/m/n' instead on input line 3. Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no h in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no ' in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no Q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no 1 in font nullfont! Missing character: There is no 1 in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no j in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no ' in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 3. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 3. Missing character: There is no , in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no . in font nullfont! Missing character: There is no A in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no g in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (32.50003pt too wide) in paragraph at lines 3--5 []\/cmr/m/n/10 ^^RA [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^o [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^o [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Ra [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] Overfull \hbox (18.91605pt too wide) in paragraph at lines 3--5 \OML/cmm/m/it/10 p[] \/cmr/m/n/10 = [] Overfull \hbox (35.55566pt too wide) in paragraph at lines 3--5 \OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 4\OML/cmm/m/it/10 :\/cmr/m/n/10 3805$ [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^o [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Re [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^o [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Re [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 \/cmr/m/n/10 ^^Se [] ! Undefined control sequence. l.6 $p_{\text {des}} =$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Overfull \hbox (27.81807pt too wide) in paragraph at lines 6--7 \OML/cmm/m/it/10 p[] \/cmr/m/n/10 =$ [] ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.8 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.9 -85 & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.10 -8+69i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.11 -8-69i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.12 -28+17i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.13 -28-17i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.14 -16 & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.15 -4+3i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.16 -4-3i & I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 7 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.18 \end{bmatrix} ^{T} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (258.6378pt too wide) detected at line 19 \OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 85 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 8 + 69\OM L/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 8 \OMS/cmsy/m/n/10 ^^@ \/cmr/ m/n/10 69\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 28 + 17\OML/cmm/m /it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 28 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 17\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 16 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 4 + 3\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 4 \OMS/ cmsy/m/n/10 ^^@ \/cmr/m/n/10 3\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n /10 4[] [] ) ! Emergency stop. <*> Q17.tex *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 41 strings out of 474222 746 string characters out of 5748733 1923975 words of memory out of 5000000 22394 multiletter control sequences out of 15000+600000 558377 words of font info for 37 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 23i,3n,32p,266b,133s stack positions out of 10000i,1000n,20000p,200000b,200000s ! ==> Fatal error occurred, no output PDF file produced!