HW#\t5-\tPg\t1 Homework\t-\t#5 APSC\t179\t-\tLinear\tAlgebra\tFor\tEngineers Due:\tby\tNoon\tin\tthe\tdrop\tbox,\tFeb\t28th,\t2017 Q1)\tUsing\tstandard\tcoordinates\tand\ttransformation\tof\tthe\tstandard\tbasis\tmethod, create\ta\ttransform\tthat\twill\tshear\tthe\tx\taxis\tby\ta\tfactor\tof\t(0.5)y,\t(ie\tx\t=\tx+0.5y)\tand scales\tthe\tz\taxis\tby\ta\tfactor\tof\t3.\t(Show\tthe\tmethod\tnot\tjust\tthe\tanswer.) Q2)\tThe\tleft\thand\timage\tbelow\tof\ta\tstudent\tdoes\tnot\tproperly\trepresent\ta\t179 student. a)\tFind\ta\tseries\tof\ttransformations\tto\tconvert\tthe\tfrown\tto\ta\tsmile. You\tmay\tuse whichever\tcoordinate\ttype\tmakes\tthe\tmost\tsense\tto\tuse. The\tarc\tfor\tthe frown/smile\tis\trepresented\tby\ta\tset\tof\tthree\tpoints. b)\tCombine\tthe\tabove\tseries\tof\ttransformations\tinto\ta\tsingle\ttransformation\tthat performs\tthe\tsame\tset\tof\toperations\tin\tone\tmatrix\tmultiplication. c)\tShow\tthat\tyour\ttransformation\tworks\tby\tapplying\tit\tto\tthe\tpoints\tin\tthe\tsmile. HW#\t5-\tPg\t2 Q3)\tThe\tyear\tis\t2017,\tand\tyou\thave\tall\tdecided\tto\tenter\tthe\t5th\tAnnual\tTrebuchet Competition,\tput\ton\tby\tthe\tengineering\tstudent\tsociety. To\tspice\tthings\tup,\tthe organizers\tare\trequiring\tyou\tto\tshoot\twithout\tbeing\table\tto\tsee\tthe\ttarget. You\tare able\tto\thave\ta\tspotter,\twho\thas\tclimbed\ta\ttree\tfor\ta\tbetter\tview.\tGiven\tyour\tnewly minted\tlinear\talgebra\tskills\tyou\tare\tready\twin\tthis\tthing. zt 30m Target xt yt xs zs ys 50m zy yy 5m Your SpoFer 50m xy You\twith\tyour\ttrebuchet a)\tFind\tthe\ttransform\tto\tconvert\tcoordinates\tfrom\tthe\ttarget's\tperspective\tto\tyour spotter's\tcoordinate\tframe. b)\tFind\tthe\ttransform\tto\tconvert\tcoordinates\tfrom\tthe\tspotter's\tperspective\tto\tyour coordinate\tframe. c)\tNow\tcombine\tthe\ttransforms\tto\tget\ta\ttransform\tthat\twill\tconvert\tcoordinates from\tthe\ttarget's\tperspective\tto\tyour\tcoordinate\tframe. d)\tWhat\tare\tthe\tcoordinates\tof\tthe\ttarget\tfrom\tyour\tperspective. (Use\tlinear\talgebra don't\tjust\ttake\tit\tfrom\tthe\tfigure.)