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Question 2 |3 Mark|: Consider the following system of linear equations: 3.333(1t. + 15920x3 + [0.333; = T953. 2.222(1r. + 16.1104} + 9.6[203'3 = 0.965. -l.561|.t. + 5.l792.r2 - [.6355x3 = 2.7M. with actual solution: [1, 0.5, -1]. it. Use Gaussian elimination and three-digit rounding arithmetic to solve the above linear gm compare the approximations to the actual solution. b. Repeat the exercise using Gaussian elimination with partial pivoting. c. Repeat the exercise using Gaussian elimination with sealed pivoting. 26. Let U = {arithmetic, algebra, calculus, geometry, trig- onometry, analysis, topology, statistics), B = {analysis, topology, calculus), C = {algebra, calculus, trigonom- On alleast smoe a2go etry, analysis}, D = {arithmetic, algebra, calculus, of it bus 19931himtopology, statistics), E = {algebra, calculus, geometry, In Sigbol bos .onill s trigonometry, analysis). In each of the following, repre- sent the given set by an array of zeros and ones. un Blonet (a) BUG work (b) COD J ad qual bas silo (c) Bn (DnE) (d) BUE end ow slegs bas .at (e) Cn(BUE)Note: for statistical mechanics problems, you may use the following numbers of congurations] microstates depending on the phase of the system (ideal gas, 9, liquid, 1, or solid, 5): 1. Communal Entropy. The difference in entropy upon melting of a solid is commonly referred to as the "communal entropy," and for a crystalline solid is predominantly due to the difference in congurational entropy of the resulting liquid (denoted by I) compared to the initial solid (denoted by s): rms 2' sdlsconfig = configJ Sconfig Use statistical mechanics to find a simple expression for drugs by assuming that the molar (or molecular) volume of the solid and liquid are approximately equal. Hint: you will need to employ Stirling's formula (Equation 1.? in Simon 9 McQuarrfe). 4. One of the computational chemical methods used to determine the energy of a compound is Molecular Mechanics. Molecular mechanical equations are stated as follows: E= [ko(T-To)? + [ko(0-8.)? + 41+ cos(nt - ] lori + EET 919 1 + + (a) Explain the meaning of each term in the equation above so that it can be explained the contribution of each component determining the amount of energy. (b) Describe the strengths and weaknesses of molecular mechanics methods in determining the properties of compounds