Para cada uno de los siguientes grupos, encuentra un grupo donde el grupo dado sea un subgrupo normal distinto del total. S3 A4 S4 Please be as clear as possible showing and explaining all the steps, and use definitions if necessary. Thank you very much

Q: Let R be a ring in which each element is idempotent. Let R = R XZ₂. Define + and x on R by (a, [n])…

A: Given: R is a ring in which each element is idempotent and R=R×Z2.To show: + and × are well-defined…

Q: dy Use the substitution x = e to transform the given Cauchy-Euler equation to a differential…

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Q: In Exercises 19-20, find TÂ(x), and express your answer in matrix form. 1 2 ^= 3x-[-] ; X= 4 19. (a)…

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Q: 9.) Find the function whose 2nd derivative is given by f"(x) = 1 - 4x where f(−1) = 1, and f(-1) =…

A: Given that , f''(x)=1-4x  ------(1) Now integrating both sides of (1) with respect to 'x' we get,…

Q: B: Find Inverse Laplace Transformer for the following function:- 3s3-s²-3s + 2 S² (S-1)² F(s) =

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Q: Evaluate the triple integral III f(x, y, z) dV over the solid E. f(x, y, z) = e√x² + y², E = {(x, y,…

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Q: Let b₁ = [3] and b₂ = H [T]B= The set B = (a) The matrix of T relative to the basis B is {6₁, 62₂} i…

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Q: 2: Find: 1 [53 - 3] L-1[:

A: We are required to find the inverse Laplace transformation of the function 1s3-a3 i.e. ℒ-11s3-a3 .…

Q: Consider the following expressions as functions of a with domain equal to the open interval (0, 1)…

A: Domain of the function is 0,1, codomain is ℝ The function is bounded attain  and attains absolute…

Q: For the following boundary-value problem (BVP): d'u dx² subjected to the boundary conditions Obtain…

A: Using laplace transform

Q: Evaluate 3y1+y³ dA where D is the region described by: D ≤ y ≤ 2,0 ≤x≤ 6. Enter an integer or a…

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Q: T Use spherical coordinates to find the volume of the ball p < 3 that is situated between the cones…

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Q: B: Find Inverse Laplace Transformer for the following function:- 3s³-s²-3s + 2 3 S² (S-1)² F(s) =

A: I have explained everything with in the solution. Please go through that.

Q: 6. State two ways to determine whether or not an n x n matrix A is invertible.

A: To Do: State two ways to determine whether or not an n×n matrix A is invertible. Also, solve…

Q: Find all critical points of the following function. x³ y³ 3 3 f(x,y) = 3 + 8xy

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Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o,…

A: X=o,p,s,wY=a,b,e,g,kZ=1,2,3,5,7,9f:X→Yf=o,a,p,g,s,e,w,bg:Y→Zg=g,3,e,2,b,9,k,7,a,1

Q: Compute COT(Σ?31 COT-1(1 + Σ=12k)

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Q: Exercises 1-4 display sets in R². Assume the sets include the bounding lines. In each case, give a…

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Q: The graph shows a region of feasible solutions. Use this region to find maximum and minimum values…

A: We will find the value of objective function at corners points because we know maximum and minimum…

Q: In Exercises 15-18, let W be the set of all vectors of the form shown, where a, b, and c represent…

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Q: Convert the integral 1/2 √9 - x² LE**** √ 18-x² - y2 dz dy dx into an integral in spherical…

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Q: Find the determinant of the n × n matrix.

A: The determinant of the n × n matrix. 1-n11…111-n1…1⋮⋮⋮…⋮111…1-n

Q: The diagram shows a shape ABCD. The curve AB is an arc with centre D. Angle ADB is 0.75 rad. Find B…

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Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Given the determinants of the following matrices: 1-3 4 1 4 -3 -1 1 10 14 54 10 -6 -5 -2 5 1-5-65…

A: The value of the given determinants are

Q: -1 Let A = -1 3 2 2 x-5 Compute the determinant of A (it will be a polynomial in x) and use it to…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Give an example of how the following equations can be used in…

A: Given: A) ddxUn=nUn-1dudx, B) dCdx=0We need to give an example of how the given equations can be…

Q: Q1: A: Find the Laplace Transformer for the following function [8 sin²t cos²t] t L

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Q: Determine which sets in Exercises 15-20 are bases for R² or R³. Justify each answer. 5 10 ¹5. [-2]…

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Q: Let L₁ be the line passing through the points Q₁-(-1.-3, 1) and Q₂-(-4,-6, 2). Find a value of k so…

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Q: Find the products AB and BA to determine whether B is the multiplicative inverse of A. -2 -2…

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Q: x² + y² + z² lim (x, y, z)→(0, 0, 0) x² + 2y² + z

A: The function given is: x4+y2+z3x4+2y2+z The objective is to evaluate the limit of this function as…

Q: For each of the graphs below, use the level curves of the function z = f(x, y) to decide the sign…

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Q: Let L be the line passing through the point P=(4, -3, 1) with direction vector -[-4, 1, 1], and let…

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Q: 1 x₂(1) (2) 1 -1 0 (1)

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Q: 1. (a) Consider the matrix A: (b) Let - 2 4 1 0 6 t t 13 8 8 20 22 -1 teR. Compute the determinant…

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Q: A relation R is given in the matrix below. Rows of the matrix are numbered 1 through 4 from top to…

A: Let iRj (i,j=1,2,3,4) be the elements of relation R . Let aij be the ( i-row , j column)  entries of…

Q: 4n+1 (e) an = (²n2+5)*

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Q: By sketching the graph of y=x-x, determine the range of values for which the function x4 - 2x² is…

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Q: Consider the basis B of R² consisting of vectors Find # in R² whose coordinate vector relative to…

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Q: 88. Prove or disprove: For every natural number n, 3+6+12+...+3(2-¹)=3(2-1).

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Q: OX Find the absolute maximum and minimum of the function f(x) = 2x² + 2' on the interval [-4, 4]…

A: There are some following steps to find the absolute max and min of f(x).(a)  Find all critical…

Q: Consider the functions f(x) = 10x7, g(x) = 10x - 3 Determine the following compositions of…

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Q: Determine the sum x = a n Ek+b, where a=5, b=5, and n=20. k=1

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Q: In Exercises 21-26, evaluate det(A) by a cofactor expansion along a row or column of your choice.…

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Q: b) Let p≥ 3 be prime. Show that the only solutions to x² = 1 (mod p) are x = ±1 (mod p). Hint: Apply…

A: Given: p≥3. To Show:The only solutions to x2≡1 mod p are x≡±1 mod p.

Q: 2.) Find the absolute maximum and minimum of the function f(x) = x³ +1.5x² -6x + 3.5 on the interval…

A: The given function is fx=x3+1.5x2-6x+3.5 on the interval -4,3. To find the maximum and minimum value…

Q: K Let A = 34 -21 and B= 16 -3 k What value(s) of k, if any, will make AB = BA? Select the correct…

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Q: applied discret mathes  if |A| = 3, |B| = 2, Then what is the cardinality of the power set of A x B

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