Given a square matrix A of dimension n, which has only non-null elements in the inputs Aj1, Aji, Aji+1, Anı and Ann for all i e {1,2, .n – 1} Make a function that solves a system A, = b by the Jacobi method that uses of A and receives as parameters the Inputs: A; b; The starting point; The maximum required the structure tolerance; Maximum number of iterations. (Octave/ Matlab) Explain the steps pls.
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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BUSING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.Suppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 1
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- Determine P(A x B) – (A x B) where A = {a} and B = {1, 2}.The following problem is called the coupon collector problem and has many applications in computer science.Consider a bag that contains N different types of coupons (say coupons numbered 1 . . .N. There areinfinite number of each typ of coupon. Each time a coupon is drawn from the bag, it is independent of theprevious selection and equally likely to be any of the N types. Since there are infinite numbers of each type,one can view this as sampling with replacement. Let T denote the random variable that denotes the numberof coupons that needs to be collected until one obtains a complete set of atleast one of each type of coupon.Write a R simulation code to compute the E(T). Plot E(T) as for N = 10, 20, 30, 40, 50, 60. In the same plot show the theoretical value and summarize your observation regarding the accuracy of theapproximation.6. Let f(n) and g(n) be non-negative functions. Show that: max(f(n), g(n)) = 0(f(n) + g(n)).