Show that all automorphisms of a group G form a group under function composition. Then show that the inner automorphisms of G, defined by f : G--->G so that f(x) = (a^(-1))(x)(a), form a normal subgroup of the group of all automorphisms. For the first part, I can see that we need to show that f(g(x)) = g(f(x)) for x in
1) Solve by the addition method. 3x + 2y = 14 3x - 2y = 10 2) Solve by the addition method 5x = 6y + 50 2y = 8 - 3x 3) Solve. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4) Can't type fractions, so
1) You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? 2) A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that wil
Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?
14. 5x(x + 1)(x - 1) > 0 24. t(x) = - t(4), t(4), t(0), t(-1), and t(- ) 28. Find the domain of the function t in exercise 24. Graph. 42. f(x) = Simplify. 56. - For the given function, find the indicated function values. 60. g(x) = - g(-62), g(0), g(-13), an
2x + y + 2z = 3 x + 6y + 3z = 4 3x - 2y + z = 0
I need an explanation, with examples in R3, of the difference between a spanning set and a basis.....when can one not be the other? keywords: bases
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1) Find the degree measure of the angel marked Z 2) High-Risk Funds Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she m
4. The St. Marks community bbq served 250 dinners. a child's plate cost 3.50 and an adult's plate cost 7.00. A total of 1347.50 was collected. how many of each type of plate was served? 8. Deep thought granola is 25% nuts and dried fruit. Oat dream granola is 10% nuts and dried fruit. How much of deep thought and how much of
Let T be a tree of order at least 4, and let e1, e2, e3 belong E(T^), T^ means Complement of T. Prove that T+e1 +e2+ e3 is planar. Please, draw the graph and explain it step by step.
Prove that if T Є L(V) is diagonalizable then V = im(T) + ker(T) (+ = direct sum) (Hint: Use a basis of eigenvectors. The eigenvectors of the eigenvalue zero are a basis for the null space, and the remaining eigenvectors are a basis for the image) See attached file for full problem description. keywords: matrix
Show that 937 is an inverse of 13 modulo 2436.
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(5) Let R be a ring with 1 and M a left R-module. If N is a submodule of M, the annihilator of N in R is defined to be: {r in R/rn=0 for all n in N} Prove that the annihilator of N in R is a two-sided ideal of R.
Given the plane (x, -y, 0). This is the plane that is parallel with the Z axis and intersects the x,y plane through the line x-y=0 in 3 space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eig
Solve the system of equations graphically. Then classify the system as consistent or inconsistent and the equation as dependent or independent. 6. 2y = 6 - x, 3x - 2y =6 14. y - x = 5, 2x - 2y = 10 16. y = 3 - x. 2x + 2y = 6
Given the plane: x-y in 3-space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eigenvectors for these eigenvalues
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UNIT FIVE DB B: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: ? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? ? Which one of the basic functions (linear,
Let K={k1,....km} be a conjugacy class in the finite group G. a) Prove that the element K=k1+k2+....km is the center of the group ring R[G] (check that g^-1Kg=K for all gin G) b) Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki. Prove that an el
Find the exact expression and satisfy the following system. See attached file for full problem description. keywords: four equations with four unknowns
1. An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% profit on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork. 2. A professor
Solve each system by substitution y = 2x -8 4x + 3y = 1 solve each system by the addition method 3x + 2y = 3 4x -3y + - 13 Determine whether each system is independent, inconsistent or dependent y = 3x -5 y = 3x + 2 y = 2x -3 y = 5x - 14 Solve the following system by the elimination of variables x +
Find a linear function f(x) = mx + b whose graph has the given slope and y-intercept. 6. Slope: 4/5 ; y-intercept: (0,28) Find an equation of the line having the given slope and containing the given point 14. m = 3, (-2, -2) Find an equation of the line containing the given pair of points. 28. (-4, -7) and (-2, -1
3 problems 2x- y + z = 5 x + y -2z = -4 3x - y + 3z + 10 2x+3y - 2z = -11 3x - 2y + 3z = 7 x-4y + 4z = 14 x-y + z = 1 2x - 2y + 2z = 2 -3x + 3y - 3z = -3
Indicate whether each system is independent, inconsistent, or dependent x+3 (y-1) = 11 2 (x-y) + 8y =28
1. Find k if the following system of equations has a unique solution 2x + (k - 1)y = 6 3x + (2k + 1)y = 9 2. Find k if the following system of equations has infinite solutions kx + 3y = k - 3 12x + ky = k 3. Find k if the following system of equations has no solution 3x + 2y = 6 kx + (k - 1)y = 9
See attached file for full problem description. When converting from Fahrenheit degrees to Celsius degrees, a well known formula is used: C= 5(F - 32) / 9
See attached file for full problem description. 1. Find the slope of the line passing through the points (-8, -3) and (-2, 2). A) B) C) D) 2. Give the coordinates of the point graphed below. A) (4, 0) B) (-4, 0) C) (0, 4) D) (0, -4) 3. Find the slope of the graphed line.