1. I f A and B are normal subgroups of G such that G/A and G/B are abelian, prove that G/(A intersect B) is abelian 2. Let H and K be groups, let f be a homomorphism from K into Aut(H) and as usual identify H and K as subgroups of G= H x_f K( x_f denotes product of H and K under f). Prove that C_K(H)= Ker(f) ps. C_K(H) is
Please see the attached file first. I did the proof, but it's weak, since I can't find a way to argue why every odd order subgroup has to be a subgroup of the cyclic odd order subgroup K of index 2, and by the divisibility argument it still could be a subgroup of G and not to be contained entirely in K.
Jill, Karen, and Betsy studied a total of 93 hours last week. Jill's and Karen's study time totaled only one-half as much as Betsy's. If Jill studied 3 hours more than Karen, then how many hours did each one of the girls spend studying?
Y=x-5 3x-4 (y-2) = 28 - x Solve the following system by elimination of variables x+y-z=2 2x-y+3z=-5 x-3y+z=4 Solve system below using Cramer's rule x+y =0 x-y+2z=6 2x+y-z=1
2x-y-z=3 3x+y+2z=4 4x+2y-z=-4 2x + 3y-2z = -11 3x-2y +3z=7 x-4y+4z=14 Solve one problem below by Gauss-Jordan elimination method -x+y=1 2x-3y=-7
Indicate whether each system is independent, inconsistent or dependent Three problems 5x-3y=-20 3x+2y=7 x+3 (y-1) =11 2 (x-y) + 8y = 28 0.4x + 0.06y = 11.6 0.8x - 0.05y = 13
Indicate whether each system is independent, inconsistent or dependent x+2y=1 8x+6y=4 x-5y=4 4x+8y = -5
-2x+3y-4z=3 (four problems) 3x-5y+2z=4 -4x+2y -3z=0 x +y =7 y - z = -1 x +3z = 18 Solve Each System x + y + z = 9 x + y = 5 z=1 x-y+z=2 y-z =3 x =4
-2x +3y -4z =3 (three problems) 3x-5y + 2z = 4 -4x + 27 -3z+0 Solve each system below x + y + z = 9 x + y = 5 z = 1 x-y+z= 2 y-z=3 x = 4
X+y-z=6 (four problems) y+z=11 y-z=3 x+y+z=2 x+2y-z=6 2x+y-z=5 2x-y+z=10 3x-2y-2z+7 x-3y-2z=10 x+y =7 y- z = -1 x + 3z = 18
3x/2 - 2y/3 = 10 1/8x + 1/4y=5
Determine whether the equations are independent, dependent or inconsistent y= 3 (x-4) 3x - y = 12
Determining the equation for a matrix and confirming the inverse, eigenvalues Details: I have think the answer to question (a) is theta^2 [(1-p)I + pJ]. But when I am multiplying the sigma and the sigma inverse I still have "stuff" at the tail end of the identity......being added. I know I should be left with the identity if t
Prove that every regular tournament is strong. Hints Here we need to first figure out something more about outdegrees and indegrees and orders of regular digraphs. Try to find a regular digraps with 3, 4, 5 ,6 vertices, and generalize. D is a regular tournament if there is k such that outdegree x = k and indegree x = n-k
I'm attaching a PDF file with a question about finding nonzero subspace along with the property of direct sum. I wonder if anyone who is familiar with Advanced Linear Algebra material and can provide a detail explanation.
Graph the line: y= -4
Graph the line with slope -3/4 passing through the point (-5,-5)
Flying against the jetstream, a jet travels 1890km in 3 hours. Flying with the jetstream, the same jet travels 4650km in 5 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?
Two rainstorms occurred in one week in a certain area. In the first rainstorm 35ml of rain fell per hour, and in the second rainstorm 20ml of rain fell per hour. Rain fell that week for a total of 45 hours for a total rainfall of 1200ml. How long was each of the two rainstorms?
Graph the line: 8x - 4y - 17=0
Draw the line whose y-intercept is -7 and whose x-intercept is 4.
3.2 prove that a graph G is a forest if and only if every induced subgraph of G contains a vertex of degree at most 1. Please can you explain in here when the graph G is a forest and induced subgraph.
1. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) 2x - y = 3 2y = 4x - 6 2. (Solve system by the substitution method. Determine whether the equations are independent, dependent or inconsistent.) y = 3(x - 4) 3x - y = 12 3. (Solve sy
Solve each system by the addition method. Indicate whether each system is independent, inconsistent, or dependent. 1. -3x + y = 3 2x - 3y = 5 2. x + 3(y - 1) = 11 2(x - y) + 8y = 28 3. 1/3x - 1/6y = 1/3 1/6x + 1/4y = 0
Solve each system by the substitution method. Indicate whether each system is independent, inconsistent, or dependent. x = 1/8y - 1 y = 1/4x + 39
Two rainstorms occurred in one week in a certain area. In the first rainstorm 25ml of rain fell per hour, and in the second rainstorm 15ml of rain fell per hour. Rain fell that week for a total of 55 hours for a total rainfall of 1025ml. How long was each of the two rainstorms?
Flying against the jetstream, a jet travels 2600km in 4 hours. Flying with the jetstream, the same jet travels 6060km in 6 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?
Flying against the jetstream, a jet travels 4550km in 7 hours. Flying with the jetstream, the same jet travels 5340km in 6 hours. What is the speed of the jet in still air, and what is the speed of the jetstream?
Find the values of x and y that solve the following system of equations -7x + 2y = 2 4x - 3y = -3 See attached file for full problem description.
Solving Linear Equations. Solve for X 3/2x - 4 = 1/3x + 7/6