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(6) The center of a group G is the set ZG) = {x EG: zg = gx for all g € G}. Thus, x E Z(G) if x commutes with element of G. Prove that Z(G) is a subgroup of G. (7) An automorphism of a group G is an isomorphism from G to G. Let G be a group and let x E G. Prove that the function 4x: G + G defined by 4x(g) = xgx for all...
For the circuit be low, compute: - the input impedance Za; - the voltage Vc Zg A Vc Zoe Zoe Zc E ZA D Z.o2 YD I- Data: E-10 V (peak value) YD (0.00275-j0.00 1) S 2.8x10 m/s (for all the lines) AB 4 cm Zc-(25-j25) Q Zo2= 200 f= 7 GHz BD-1.04 cm Zg-100Q Zol 100 Q BC 3 cm For the circuit be low, compute: - the input impedance Za; - the voltage Vc Zg A Vc Zoe...
(5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4 (5) Let Ф, : Z5[x] Zg denote the evaluation homomorphism at r Zg Find a nonzero polynomial of smallest degree which in kernel of all φ-for r 0,1,2,3,4
(4) (10 points) Show that 3 is a prime element in Zg]. Find the irreducible Z8]. Specify the irreducible factors that appear in the factorization of 9t. ation of 9i in let Prime P-(3) Thus 3 divide s Nea) ar 3 divides NC) ud we can sahat divides N(O)x possibility t, Hat bof ,, hak rosidue omod 3 Henle 9ie3 and p.3 (s prime. 3, us Sethat we are left wl oor 1 , So the only if you work...
system with impulse response hn ! = un- x[n] = u[n]-u[n-4]. Compute Y(z) X(z)H(z) and use Y(z) to compute y[n].
Make up a function F: R^3 -> R^3, [f1(x,y,z); f2(x,y,z); f3(x,y,z) ] and compute its gradient. Be a little creative, give me a polynomial, some trig functions, and maybe something else. Include a cross term or two.
8. (20 points) Let G Zs x Zg and let H be the cyclic subgroup generated by (3, 3). (a) Find the order of H (b) Find the orders of g = (1,1) + H, h = (1,0) + H and k = (0,1) + H in G/H (c) Classify the factor group G/H according to the fundamental theorem of finitely generated abelian groups. 8. (20 points) Let G Zs x Zg and let H be the cyclic subgroup generated...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
At 417 K, this reaction has a K value of 0.0825. X(g) +3 Y(g) Zg) Calculate Kp at 417 K. Note that the pressure is in units of atmosphere (atm). Kp enms of use consact us help sm inoge Careors Photo Booth ptivacy policy
Use the Divergence Theorem to evaluate ∫∫S F·dS, where F(x,y,z)=z²xi+(y³/3+sin z) j+(x² z+y²) k and S is the top half of the sphere x²+y²+z²=4 . (Hint: Note that S is not a closed surface, First compute integrals over S₁ and S₂, where S₁ is the disk x²+y² ≤ 4, oriented downward, and S₂=S₁ ∪ S.)