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- Compute using Gauss-Seidel Iteration.The process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.Without doing any calculations in Aut(Z105), determine how manyelements of Aut(Z105) have order 6.
- Use the Euler algorithm with a step size h = 0.2 to find an approximate value of y10 for the linear first-order initial value problem in the interval 0 ≤ x ≤ 2 in four decimal places.Suppose that the probability of making a mistake in translation at each translational step is a small number, δ. Show that the probability, p, that a given protein molecule, containing n residues, will be completely error-free is (1 – δ)n.We want to find the number of ways in which 3r balls can be selected from 2r red ballsand 2r blue balls. Find the generating function corresponding to the above problem in closed form.
- The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(x) = 2xTn(x) −Tn−1(x) with T0(x) = 1 and T1(x) = x.a) Show that any two Chebyshev polynomials are orthogonal with respect to the weighting factor (1 − x)-1/2 in the closed interval [−1, 1]. b) Pick the first three Chebyshev polynomials and use Gram-Schmidt orthonormalization procedure to form anorthonormal set in the closed interval [−1, 1].determine how many Jordan canonical forms are with the given eigenvalues(not counting rearrangements of the Jordan blocks) and list each of them. Q. A 5×5 matrix with eigenvalues λ=2,2,2,2,2.A purchaser of transistors buys them in lots of 20. It is his policy to randomly inspect 4components from a lot and to accept the lot if at least 3 are nondefective. Suppose eachlot contains exactly five defective transisters. What proportion of lots are rejected?
- how come there is not a t-term for the multiplicity of 2 eigenvalue?Consider the 8-city traveling salesman problem whose links have the associated distances shown in the following table (where a dash indicates the absence of a link). City 1 is the home city. Using 1-2-3-4-5-6-7-8-1 as the initial trial solution, perform three iterations of simulated annealing algorithm.Prove that (1,1) is an element of largest order in Zn1 + Zn2. State the general case. Needs Complete solution with 100 % accuracy.