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MATH 1ZC3 Lecture 6: 1.4 Inverse and properties

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plumcockroach206

20 Feb 2019

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McMaster University

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Inkling trace if a is run traceofit trca isthesumofthediagnot entries. A i tr a 2 1c 4 2 trcabhtrcatkbm. Iis it trials tr ba assume bothproductaredefinedandbothabansquare fr ab weknowthatabfba beecereeer. Ba e f if i monegeneral case leta bbe n xn. The ith diagnalentry inab c f it is c fail aiz ain. Lii bi tow xaiccolnay ibii. biz bing. tl ii bikxaki. Y dummyvariable i interchangeable i trash iecik. ie birxakiffaifzxazxgbxz theanswerwouldn"tbetruebecausehesam wouldhave differentendingpoint 7,2 and y. Ab t ba r c e matrix dontcancelingeneral. At 135 ahzab1132 i ifeng. nou. otwwaei. ca faioo awwiiis b sett. If ais square thenbistheinverseofa if a13 1 andba i. B a 1 if a13 1 andba i ie aa i andaa i if bib thenit is b"sinverse similartonumbers a casewhen13a ab. Ifadoesn"thasa1 thenitiscalled noninnertable or singular eg a i 53 d 3 em. 31223151 2 5 52 t seh it a. tiieits: f ba i lo p. Pfttipy. ie fyouge tkidentity i i iiii ab bi iiii.

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be parametric esjuations for a tb) C i v i) C intersects esactly one e ine containing the point -1.3. intersects the xy and ntion voctor to find another esqua ne line with the Korm 17) Let C be the line the ine eontaining the point a) Give parametric ejuastions for c (b) Write an equation for C in on vector to find another equa for the same 18. Let C be the line deterimined by the tt (a) Provide a vector b) Give parametricequations fore c 19. Let C be the line determined by the the points where the line + bt.to t et) eplanes. Ia-0, esplain (a) Provide a vector (b) Write an equation for C in s, determine wbether the the distance between the c. 20. We wish to find the distance from C as shown in the figure that fo dinates of points P and Pa, but we do dinates of point Q (a) Ifyuknew the measure of angle Î¸ llows Wek sect, find the point of intent know th- t.5-3,6+7. weould find the distance from point P to lanes r2()3-,4+3t,5-2 Applications ne. Explain why the vation in Washington State. She tonic wastes in one of the tank tank farm is huge, and she d is leaking. Worse yet, the tank g the tanks would req tank farm, an operation that Instead, Emmy has wells dug the tank farm, to try to trace the earth's surface is conside the bottom of the tank farm the distance is given in f taminated groundwater at (1033, 247,-55). If the w of one of the tanks and i what is the location of th the line does not ow you can distance from point P to line C even if you do ne know the measure of angle Î¸. line containing use the tech- ization for the 24. P023.5), ds(23.5) 25,Pi-1, 3, 7. d = (2,0,4) the leak? eyuivalent.6. Ptbc 53. lan is climbing Mountl He has made a secon mountain. He does n 27, P3, 1), d= (2 5) 28, p(1.3,-2, 4), d= (4,-1,5, 8) In Exercises 29-34, find an equation of the line containing the Proofs ntaning the given pair of points. Express your answer (a) as a vector p ess your an- rametrization, (b) in terms of parametric equations,and ( n 54. Let Ci and C be line symmetric form. 29. P(O,0,0), Q(4,-1,6) and P2 and Qa poin C2 if and only if P â¢P(3,-1,7), Q(5,8,-2)