Solve the following system of linear equations using LU decomposition. Show each step including the decomposition process, forward and backward substitutions, and verification of solutions. (1) X1 + X2 + X3 = 13, (Il) X1 - X2 + X3 = 6, (Ill) X1 + X2 - X3 = -3O CONNECTIONS TO THE REAL WORLD Each of the changes you observed represents a real process that you probably have seen or heard about. Your instructor will provide you with an Atom Key to help you identify what processes are occurring in each of the Changes in Chemistry cards. Below are descriptions of each of these processes in some real-world situation. Match each Changes in Chemistry card with the appropriate description. Road salt, sodium chloride, is commonly used to de-ice roads during the winter. When road salt dissolves in the water on the road, it reduces the temperature at which the water would freeze. This helps prevent ice from forming on the roads. Cars have been made from steel, which is mostly iron, since their introduction into society in the early 20 century. When the iron interacts with oxygen, it forms rust. This problem is accelerated by the wet, salty roads in many cold, winter climates. Copper has been used by humans for about 10,000 years. Due to its excellent flexibility and great ability to conduct electricity, copper is used for electrical wires as well as in pipes for plumbing Original camera "flash bulbs" consisted of very fine magnesium filaments. An electrical current, triggered by the camera shutter, heats the filament until it ignites and burns, very quickly and brightly, with the oxygen in the air. Before the invention of the refrigerator, perishable food was often kept in ice boxes, which were cooled using blocks of ice. People relied on ice boxes even during the summer months. Ice was often stockpiled in large "ice houses" during the winter and could often be kept from melting until the following winter. Henry Cavendish is credited with identifying hydrogen gas as a unique element in 1766. Cavendish produced hydrogen gas by combining a metal, such as magnesium, with a strong acid, such as hydrochloric acid. Hydrogen production soon became useful as balloonists found this "lighter than air" gas quite useful. Sodium bicarbonate, commonly known as baking soda, is used to make baked goods light and fluffy, It does so by decomposing to produce water vapor and carbon dioxide gas. This decomposition process is initiated by the presence of an acid, which donates hydrogen ions. 193. The normal distribution is the most important statistical probability distribution As far as practical applications are concerned; the graphical representation of the normal distribution is referred to as the normal curve. In your own words, identify three of the most important characteristics of the normal curveTable 2000 CM is based on 2000 Census data. It begins with 100,000 live births and shows how many are still alive at various ages (up to 110 years of age). The "CM" stands for cumulative mortality. These raw statistics can be used for a number of purposes. Answer each of the following independent questions relating to Table 2000 CM A. 87,595 60.6473% C 100% D. 12 40596 E. 096 F 39.35279% G. None of the other answers is correct H. 87.5959% 34.471% For each question below choose from A to I above According to Table 2000 CM, starging with 100,000 live births, how many are still living at age 60? According to Table 2000 CM, starging with 100,000 live births, what is the statistical probability of being alive at age 60? According to Table 2000 CM, starging with 100,000 live births, what is the statistical probability of having died by age 60? According to Table 2000 CM, what is the statistical probability of someone age 60 living to age 85
