use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). Partitioning large square matrices can sometimes make theirinverses easier to compute, particularly if the blocks havea nice form. In Exercises 6468, verify by block multiplicationthat the inverse of a matrix, if partitioned as shown, isas claimed. (Assume that all inverses exist as needed.)
PKSC final exam review CORRECT TESTS!!! EVALUATION FOR EXTRA CREDIT *** VAUGE review from prof HISTORY - Know timeline dates - Three M’s in definition of packaging (materials, methods, machinery) - Ancient and man-made packages - Industrial revolution o Can, celluloid, paperboard cartons - Late 20 century o 50’s 60’s, 70s, 80s, 90s - Trends - users and suppliers o users: consumer, industrial, institutional o suppliers: converters, machinery and services FUNCTIONS - contain - protect - inform/sell - utility of use* NOT IN TEXTBOOK - four levels o primary, secondary, tertiary, and quaternary - product o contents, environment, damage - inform/sell: o required, motivational, trade dress - utility of use: o consumer, retailer, shipper/distributer MATERIALS - paper and paper board – wood pulp, cellulose - metals o steel o aluminum - glass - plastic - paper o cellulose and lignin o thickness: paper vs paperboard 0.12” point .014” = 14 point o what “plastic” comes from wood Cellophane o three ways to make pulp Mechanical, chemical, and semi-chemical o general procedure for paper/paperboard Screen, squeeze and dry o Callenderig o Basis weight of paper o Etc. o Use for bending grade board o Three basic design styles for folding cartons o Tube, tray and hybrid - Testing Mulllen bursts and edge crush test - RSC Regular slotted container - Two basic styles of composite cans o Convolute and - METALS o Cans- steel and aluminum o Two basics kind of can: three and two pieces o Etc. o Plating weights measured in lbs/basebox o Three ways to seal the side seam of a three piece can Weld, solder or adhesive o Bayer process – bauxite ot aluminum o Hall herlout process o Now thin is aluminum foil 6 mil o Is aluminum used for packaging as a pure metal NO o What happens to WVTR as thickness of foil decreases Why Increases bc pinholes - GLASS o How to make glass bottles Blow and blow, press and blow o Major ingredients o What is cullet o Two methods for making glass bottles o What is gob o What is annealing Why important o Parts of a bottle o Advantages/disadvantage - POLYMERS o What is gutta percha o What is the first synthetic plastic Bakelite o Etc. o Name of chem reaction used to link monomers Polymerization o If you link different monomers o Know abbrev : HDPE, LDPE, PP, PET, PVC, PVDC(saran) o What is density Yield How related o Thermoset/thermoplastic o Cost- more specialized plastics are more costly Since the basic structure of most common polymers are similar, what mades each one different Side chains o What basic process is used for all types of forming methods Extrusion – melting plastic o What are 2 ways to make film Cast and ring die o What does orientation meant as it relates to film Stretched to align molecules for strength o What is coextrusion and what is it used for Blends different polymers, film, sheet and bottles o What is injection molding used for o What type of package does extrusion blow molding produce Bottle o What is a parison Hollow tube inflatd into bottle o How is wall thickness controlled during extrusion blow molding Programmed parison o What types of package are made by injection bow molding Bottles o Stretch blow molding Bottles o What are two advantages of extrusion bow ad molding compare to IBM and ISBM One mold and handles o Adv. And disadv. - FORMS o Rigid – glass bottle o Semi rigid - squeeze ketchup bottle o Flexible – bread bag or potato chip bag o Types of closures, indention seal, child resistant, tamper resistant, decorative etc o Dimensional analysis – what is meant when the film converter…. o Properties of laminates: structural barrier o Two ways to form a pouch: V/F/F/S and H/F/F/S o How perrmiation happens o Levels of packaging Primarty secondary tertiary quaternary o What are 3 basic areas of testing Quality, environmental, shipping and abuse (distribution and transportation) o Know the areas of testing and the specific tests o Know how to solve problems relating to stacking strength PACKAGE MACHINERY - Line function - Line speed - What really counts Output - Know how to solve problems related to lines peed - What are 2 main types of fillers o Constant level o Constant volume - How do they differ GRAPHICS AND PRINTING - Package design consists of two components… - Three fundamental messages a package must anser o What is this o What will it do fo rme o Who guarentees this - 4 basic methods of printing - What are the 4 types of package development projects - What are two development paths for pkg development DEVELOPMENT - Wht oart of a company drives development PACKAGING LAWS AND REGS - CFR - Laws and regs form all years ENVIROMENTAL LAWS AND REGULATIONS - What are the 2 main types of environmental laws and regs o Health laws – fed o Enviro – state and local o Man laws indirectly related to pkg o Mandatory recycling laws o Know modification for packaging Degradable, high cone, pull tabs - Packaging is the largest contributor of solid waste 30% - Wht is solid wastes hierarchy or disposal - Know the plastic recycling codes (1-7) - What does innovation do o Boost sales o Changes consumers demands o Change with tech developments - What is the # one factor driving innovation o Convenience!