(c) Use Euler's Theorem and part (b) with a suitable value of p to find the remainder of 5103 when divided by 14 I
Q: dice → In the experiment of throwing two fair let (A) be the event that the is odd, (B) Be the event…
A:
Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the…
A: First calculate f'x.
Q: Let x₁, x₂ denote the variables for the two-dimensional data summarized by the covariance matrix,…
A: As per the question we are given a covariance matrix along with ots eigenvalues & eigenvectors,…
Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…
A: Given function is y=x2+4x−5. We have to find the first derivative if the given function at x=0 using…
Q: log (x+3) 2+1-1-cosh (cos-¹x) lim
A:
Q: Evaluat the integral. i's ex dedy ३५
A:
Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…
A: Given that The courier will deliver if the length plus girth does not exceed 108 inches.…
Q: a x In the experiment of tussing a fair coin is the randam variable giving 3 times the number of…
A: Given three fair coins are tossed. So PX = 0 = 18P(X = 1) = 38P(X = 2) = 38P(X = 3) = 18
Q: Question 1 For the systems below, find and classify the critical points using linear stability…
A: 1. (a) Given system is dxdt=x2+y2-1, dydt=xy To Find and classify the Critical Points of above…
Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…
A: Given, box is rectangular. Let the shorter side be b (variable for square end) Then according to…
Q: Find the value of F(s) given that; sin 3t, o<t<tπ f(t) = { sin 3t, t<πT Let L[sinzt u(t)-sin3(t…
A: Use the definition to find the Laplace transform of the function sin3t ut-sin3t-πut-π.
Q: Answer the following problems using the specified method up to four (4) iterations only. Round off…
A:
Q: Let a = e =es and consider the set U₁8 = {1, a, a²,..., a¹7}. Give the elements of U18 (as powers of…
A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
Q: Write f(z) = Im(z 32) + zRe(z²) 5z in the form f(z) = u(x, y) + iv(x, y).
A:
Q: (1 Let f be integrable on [a, b]. Suppose c ER and g: [a+c,b+c] → R such that g(r)=f(z−c), x€[a+cb+c…
A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…
Q: QUESTION 2 Mei has taken out a $95,000 mortgage that has an interest rate of 4.7%. If the loan is…
A: Given:Loan amount = $95,000 , Time = 15 years , Annual interest rate = 4.7%
Q: The eigenvalues are A₁ < A₂ <3 < A4, where X₁ has an eigenvector eigenvector = A = -37 15 0 0 -70 28…
A:
Q: Given vectors (A = a₁ + a₂) and (B = 2a,- 2ay - a₂), when A is defined by Q (1,1,1) find (i) AXB…
A:
Q: -13 2 6 1 The matrix I 09 4 3 3 2-8-1 -2 3 2 10 The Augmented matrix is as follows: -13 2 6 1 -7 09…
A: Given: -13w+2x+6y+z=-7 0w+9x+4y+3z=4 3w+2x-8y-z=-5 -2w+3x+2y+10z=0 To solve the system of…
Q: Consider a system of linear equations A [:] b where -2 6-3 b = and A-1 Find the value of y in the…
A:
Q: Free Response Show all your work to support your final answer and 1. Let R be the region in the…
A:
Q: (i) Draw the graph whose adjacency matrix is given in Fig. 2.25. (ii) Draw the graph whose incidence…
A: We have to Draw the graph whose adjacency matrix is given in Fig. 2.25. and Draw the graph whose…
Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…
A: Given: Properties of a function f(x) are given below, To find: Relative maximum points, relative…
Q: Prove that the subgroup {o ES5o (5) = 5} of S5 is isomorphic to $4.
A: The given question is related with abstract algebra. We have to the subgroup σ ∈ S5 | σ5 = 5 of S5…
Q: line integral x³ dy), where y is t 3 X counter clockwise.
A:
Q: . What is the coefficient of ?^4 when (3+4x^2)^3 is expanded?
A:
Q: Let n P₁ P2 = ppp be the prime factorisation of an integer n > 1. 1: ti A 11. C.
A:
Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cos t) k…
A:
Q: Integrate the following functions f(x₁y) = (x-1) R: y=x over the given regions y=x²
A:
Q: where Su₁(x, t) = Urr(x, t), [u(x,0) = g(x), 1, g(x) = |0, = TER, t> 0, |x|≤1, x>1.
A:
Q: A Suppose A € M₁ (R)and B. Find the eigenvalues of B = [ = [2lin in terms 2A of the eigenvalues of…
A: Given A∈MnR and matrix is B=0AA2A. We have to find the eigenvalue of B in terms of A. The eigenvalue…
Q: Find d(u, v), if u = (2, -4,2,-1,-6) and =(4,-6,2,-1,-6). OA √93-√61 O B. √300 OC √73 OD. V8 O E √32…
A:
Q: How many strings of three decimal digits (each digit can be 0-9) do not contain the same digit three…
A: Solution :-
Q: Find d(u, v), if u = (2, -4,2,-1,-6) and =(4,-6, 2,-1,-6).
A:
Q: Below are the jersey numbers of 11 players randomly selected from a football team. Find the range,…
A: Use the given data.
Q: If A = [1 31 (67] 0 A. 3300 OB. -900 OC. 900 OD. 1 O E. -1 find the (1,2)-entry of A300
A:
Q: Are the vectors v1 = (2, 0, -1), v2 = (4, 0,7), and v3 = (-1, 1, 4) linearly independent in R3 ? O…
A:
Q: a)Consider the following data: 3 is a quadratic residue for 23 and 37. 3 is a quadratic nonresidue…
A:
Q: consider that; sin²t has the t 00 forem L[ f(t)] = F(s) ds with S f(t) = sin²t. Find F(s) in order…
A:
Q: A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling…
A:
Q: (-3,0) 3 -2 4- 3+ 2. -1 (0, -0.5) -1,-2) (-1,-3) -3- (1,0) 2 y = f'(x) 3 (2,-0.5) (3,-2) (4, -3) I
A:
Q: A farmer plans to fence in a rectangular pasture adjacent to a river (see figure below). The pasture…
A:
Q: For the equation, 9x² +8/3xy + y²-8=0, complete the following questions. a. Rewrite the equation in…
A: The general form of a conic equation is Ax2+Bxy+Cy2+Dx+Ey+F=0. If B2-4AC>0, then the conic is a…
Q: V. Given: 2. Find f'(2), if it exists. el3r-6-2, f(x)=[2x - 5], √x²-9, if r ≤ 2 if 2 3
A: Given fx=e3x-6-2,if x≤22x-5,if 2<x≤3x2-9,if x>3
Q: 1. Find the solution for dt² series solution.) - 2t + 4y = 0 with the initial conditions y(0) = 1,…
A:
Q: Determine in polar and Cartesian forms (a) [3/41°]* (b) (-2-)5.
A:
Q: Find the exact length of the curve. y = √x - x² + sin 1-² (√x) Read It Need Help? Need Help?
A: Solution:
Q: 2) (2x + sin x) dx + x cos y dy = 0 3) - 2y + a = 0 dx dy 3y 4) r2 (Exact). (Separation variables).…
A: according to our guidelines we can answer only three subparts, or first question and rest can be…
Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…
A:
Q: Suppose that u, v, and w are vectors such that Evaluate the given expression. u-v-2w, 4u+vi (u, v 2,…
A:
Abstract Algebra
Please don't use the Chinese remainder theorem
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
- Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic group of order n. Prove that G has elements of order 12 but no element of order greater than 12. Find the number of distinct elements of G that have order 12.The alternating group A4 on 4 elements is the same as the group D4 of symmetries for a square. That is. A4=D4.Exercises 10. For each of the following values of, find all subgroups of the cyclic group under addition and state their order. a. b. c. d. e. f.
- 27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.Exercises 8. Find an isomorphism from the group in Example of this section to the multiplicative group . Sec. 16. Prove that each of the following sets is a subgroup of , the general linear group of order over .Let G1 and G2 be groups with respect to addition. Define equality and addition in the Cartesian product by G1G2 (a,b)=(a,b) if and only if a=a and b=a (a,b)+(c,d)=(ac,bd) Where indicates the addition in G1 and indicates the addition in G2. Prove that G1G2 is a group with respect to addition. Prove that G1G2 is abelian if both G1 and G2 are abelian. For notational simplicity, write (a,b)+(c,d)=(a+c,b+d) As long as it is understood that the additions in G1 and G2 may not be the same binary operations. (Sec. 3.4,27, Sec. 3.5,14,15,27,28, Sec. 3.6,12, Sec. 5.1,51) Sec. 3.4,27 Prove or disprove that each of the following groups with addition as defined in Exercises 52 of section 3.1 is cyclic. a. 23 b. 24 Sec. 3.5,14,15,27,28, Consider the additive group of real numbers. Prove or disprove that each of the following mappings : is an automorphism. Equality and addition are defined on in Exercise 52 of section 3.1. a. (x,y)=(y,x) b. (x,y)=(x,y) Consider the additive group of real numbers. Prove or disprove that each of the following mappings : is an isomorphism. a. (x,y)=x b. (x,y)=x+y Consider the additive groups 2, 3, and 6. Prove that 6 is isomorphic to 23. Let G1, G2, H1, and H2 be groups with respect to addition. If G1 is isomorphic to H1 and G2 is isomorphic to H2, prove that G1G2 is isomorphic to H1H2. Sec. 3.6,12 Consider the additive group of real numbers. Let be a mapping from to , where equality and addition are defined in Exercise 52 of Section 3.1. Prove or disprove that each of the following mappings is a homomorphism. If is a homomorphism, find ker , and decide whether is an epimorphism or a monomorphism. a. (x,y)=xy b. (x,y)=2x Sec. 5.1,51 Let R and S be arbitrary rings. In the Cartesian product RS of R and S, define (r,s)=(r,s) if and only if r=r and s=s (r1,s1)+(r2,s2)=(r1+r2,s1+s2), (r1,s1)(r2,s2)=(r1r2,s1s2). a. Prove that the Cartesian product is a ring with respect to these operations. It is called the direct sum of R and S and is denoted by RS. b. Prove that RS is commutative if both R and S are commutative. c. Prove that RS has a unity element if both R and S have unity elements. d. Give an example of rings R and S such that RS does not have a unity element.
- Consider the group U9 of all units in 9. Given that U9 is a cyclic group under multiplication, find all subgroups of U9.Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.In Exercises 3 and 4, let G be the octic group D4=e,,2,3,,,, in Example 12 of section 4.1, with its multiplication table requested in Exercise 20 of the same section. Let H be the subgroup e, of the octic group D4. Find the distinct left cosets of H in D4, write out their elements, partition D4 into left cosets of H, and give [D4:H]. Find the distinct right cosets of H in D4, write out their elements, and partition D4 into right cosets of H. Example 12 Using the notational convention described in the preceding paragraph, we shall write out the dihedral group D4 of rigid motions of a square The elements of the group D4 are as follows: 1. the identity mapping e=(1) 2. the counterclockwise rotation =(1,2,3,4) through 900 about the center O 3. the counterclockwise rotation 2=(1,3)(2,4) through 1800 about the center O 4. the counterclockwise rotation 3=(1,4,3,2) through 2700 about the center O 5. the reflection =(1,4)(2,3) about the horizontal line h 6. the reflection =(2,4) about the diagonal d1 7. the reflection =(1,2)(3,4) about the vertical line v 8. the reflection =(1,3) about the diagonal d2. The dihedral group D4=e,,2,3,,,, of rigid motions of the square is also known as the octic group. The multiplication table for D4 is requested in Exercise 20 of this section.
- In Exercises 3 and 4, let be the octic group in Example 12 of section 4.1, with its multiplication table requested in Exercise 20 of the same section. Let be the subgroup of the octic group . Find the distinct left cosets of in , write out their elements, partition into left cosets of , and give . Find the distinct right cosets of in , write out their elements, and partition into right cosets of . Example 12 Using the notational convention described in the preceding paragraph, we shall write out the dihedral group of rigid motions of a square The elements of the group are as follows: 1. the identity mapping 2. the counterclockwise rotation through about the center 3. the counterclockwise rotation through about the center 4. the counterclockwise rotation through about the center 5. the reflection about the horizontal line 6. the reflection about the diagonal 7. the reflection about the vertical line 8. the reflection about the diagonal . The dihedral group of rigid motions of the square is also known as the octic group. The multiplication table for is requested in Exercise 20 of this section.Let p and q be distinct prime numbers and set n = pq. Find the number of generators of the cyclic group Zn. [Hint: It may be easier to first consider which elements do not generate the group]2. Find all of the abelian groups a) of order 200 up to isomorphism b) of order 720 up to isomorphism