9, X = 3, 4, 5, and 7; compute Σ, (ΣΧ), and ΣΧ2 10. X EX --3, 0, 1, and 2; compute Σ(X-1), and D3-3 11. X-3,4,5, and 7; Y-1,0,1, and 2 compute ΣΧΥ and (DIP X-3, 4, 5, and 7; Ys-1,0,1, and 2; compute ΣΧ'ya and Σ(X-2)(Y-3) 's 4, 5, 6, and 9; Y -1,-1, 1, and 2; compute ΣΥ2 and Σ(X-5)(Y+ 1) 12. 13.
of 89 SC 1& S 9 86 OF -10 -9 8 7 6 5 4 3 3 4 5 6 7 8 9 10 Submit Answer Oy = -f(x - 1) Oy = f(-x) +1 Oy= -f(x+1) Oy = f(-x) - 1
Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7→ n + 1 − i. (c) Show that this initial configuration of the 15 puzzle is not solvable 3 1 15 13 2 8 5 9 12 7 11 4 14 6 10 − (d) Suppose that (i, j) ∈ Sn is a transposition and that i < j. Find an expression (in terms of i and j...
4 machines and 9 jobs Jobj 1 2 3 4 5 6 7 8 9 Pj 4 9 3 3 6 8 8 12 6 Determine a schedule that minimizes the makespan of the following jobs on 3 machines. a) Compute Cmax(LPT) b) Pair the jobs 1-5, 2-6, 4-5, 7-8-9 • What is Cmax? • Is this Cmax(OPT)? Why? c) What is Cmax(LPT)/Cmax(OPT) ?
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 = 13 2 Also let v= 0 5 3 10 -6 0 11 1 1 7 a) (4 pts) Compute prw(v) where W = Span{u1, U2, U3} CR5. b) [4 pts) Compute prw(v) where w+ denotes the orthogonal complement of W in R5. c) [3 pts) Compute the distance between v and W.
Q1 lf S-(Q 1, 2, 3, 4, 5, 6, 7, 8, 9} and A-|0, 2, 4, 6, 8], B (1, 3, 5, 7, 9), C (2, 3, 4, 5), and D [1,6,7], list the elements of the sets corresponding to the following events: (a) A U C; (b) An B; (d) (C' n D) U B; (e) (s n c)' (f) Anc n D'.
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(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
f(t) -S -8 -7 -3 --1 3 5 1 2 13 4 7 8 9 12 t(ms 15 16 4. For the above periodic signal f(t), specify the symmetry (if any) and determine all coefficients as well as the value for w, so as to find the Fourier series representation of f(t) in the following forms. (24 pts) GO A. f(t) = a + ancos(not) + b sin(nw.t): B. f(t) = R-Cneinwor. n=1 Type A
What is this molecule? Please show all work for C6H12O d (131.3) s(a2) (381) d s.1 19 2 5 4 ppm 6 8 3 5 7 9 d (131.3) s(a2) (381) d s.1 19 2 5 4 ppm 6 8 3 5 7 9