1 Let ū = and ū = a. Prove that the set W consisting of all vectors in Rª that are orthogonal to both ữ and i is a subspace of Rª. b. Find a basis for W.

Q: Let p1(x) = x - 2020x² + b,x +c, and p2(x) =x' - 2021x + b,x + cz be polynomials having two common…

A:

Q: Ql: what's the relation between prime and semiprime ideals.

A:

Q: by a nilpotent element of a ring R? Find all nilpotent Q16: What's mean elements of Zg-

A:

Q: ) Consider The system -3 ste. al Find a fundamental matrix for thingys t 6 f the syetem Find the…

A: Consider the system of differential equations is        x'(t) = Ax              ..............(1)…

Q: Let A be an nx n matrix over C". Let A be an eigenvalue of A. A generalized eigenvector x € C" of A…

A:

Q: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1< 15}. Define a relation R from X to Y…

A: ANSWER ONLY ASAP! What are the elements of the Cartesian product X x Y?

Q: TEXT ANSWER Question 9 Given the similar prisms pictured below, with the measure of one pair of…

A:

Q: Problem 1.58 Check the divergence theorem for the function v = r? sin© î + 4r² cos e ê + r² tan 0 @,…

A: (1) Solution:- Using the volume of icecream cone shown in figure

Q: . If a permutation 7 = 0102030m where the a,'s are disjoint then the inverse of 7 is 7- = o oj = (i,…

A:

Q: 5: (A) Prove that, every group of prime order is cyclic.

A:

Q: Chelsea sets off on her hike from the lodge at a bearing of S70°W. After 3.6 miles, she changes her…

A: Solution :-

Q: Q14: Define subring. Is the set S = {(“ } is a subring of the ring M of all 2 x 2 matrices?

A:

Q: Solving bernoulli differential equatioh dy xy=XY

A:

Q: Let T : P2 → P2 be the linear transformation such that T(1) = 4+ 2x + x², T(x) = 3x, T(x²) = 1+2x +…

A: The matrix is diagonalizable if and only if the algebraic and geometric multiplicity of each…

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A:

Q: IM 6.15 1. Write another function that has the same graph as y = 2 cos(2) – 1. 2. Describe how the…

A: IM6.15 (1) To write: Another function that has the same graph as y=2cos(x)-1. (2) To Analyze:…

Q: Reading Question 6.3.4. Let G = (g) be a cyclic group of order n. Which of the following claims is…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.

Q: Find the interval of convergence for the follov ing power series E(coth n)x" n=1

A:

Q: Suppose we have the following sets: J = N, K = {k E Z | 0 < 2k +1 < 20}, L = {0, 1, 2, 3, 4, 5, 6,…

A:

Q: Find the plane determined by the intersecting lines. z=1- 3t z = 2-2s L1 x= - 1+2t y = 2+2t L2…

A:

Q: In parts (a)- (e), involve the theorems of Fermat, Euler, Wilson, and the Euler Phi-function. (a)…

A:

Q: Q3: (A) Prove that 1. There is no simple group of ord er 200. 2. Every group of index 2 is normal.

A:

Q: Problem 3 Let f(r) = x² + r. Use the limit definition of the derivative to compute f'(2). Find an…

A:

Q: 2x 1+ 2e dx

A:

Q: Solve for X. -4 -4 -6 8 -2 X+ 3 -6 Х. -3 -2 6 6. 9

A: We solve for X by using properties of Matrix.

Q: 6. A solution contains 2.12 moles of NaCl dissolved in sufficient water that has 1750grams mass.…

A: Solution: Given,   moles of solute(Nacl) = 2.12 moles               Mass of solvent (water) = 1750 g…

Q: 4. Find the isolates singularities of the following functions, and determine whether they are…

A:

Q: n n-r+1 (a) Prove that "C, =""C,-1 (b) Prove that "C, r

A:

Q: (B) Let I be a maximal proper ideal of commutative ring with identity R. Prove that R/I is a field.

A: Suppose, first, that I is an ideal of R such that R/I is a field. Since R/I is a field its only…

Q: Let a be an integer. ki k2 (a) Explain why if a? 1,.. ki ... pir, then k; is even for each prime p,…

A: The detailed solution using basic properties of divisibility is presented in the next step.

Q: 2. F(s) (s-2)(s-4)(s-8) s2 3. F(s) s4+16

A:

Q: Qs: (A) Let R be a ring with identity. Define g: Z → Z by g(x) = x. 1, Vx E Z. Is ga homorphism?…

A:

Q: Solve for A: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right…

A: We use properties of matrices.

Q: Given the demand function   P = 12.5e0.04Q   Determine the quantity Q and price P at which total…

A:

Q: السعلهلتمـِxله ملتلعللمو ) محلموكلوفحلرللت )رههد x^(5- )x = )ه ,4¢x

A: The given P.D.E is                              utt=16uxxu0,t=u5,t=0, utx,0=0   ux,0=x25-x To find:…

Q: Instructions: For every item given below, determine which kind of algebraic structure it is, and…

A: Given: 5) a∈A 6) a,b∈A To find: Table

Q: L{5u(t – 3)} = where u is the unit step function a. 5e3s 5e-as b. 5(t-3) C. d. 5e-3s е. 5ut - 15и

A:

Q: D=(1, 2, 3} F= (1, 2, 3, 4, 5, 6, 7, 8, 9, 1

A: Introduction: If Set B contains at least one element that is not present in Set A, Set A is…

Q: P and Q are two points on either side of the parallel lines AB and CD so that AB lies between P and…

A:

Q: Q;: A. Let G be a group. Show that G is abelain iff the mapping f:G→G defined by f(x)=x", VxeG is an…

A:

Q: Characterize the primes p mod 20 such ial

A: We have to characterize p mod 20 such that -5p=1.

Q: Solve the following harmonic sequences. 1. What is the ninth term of a harmonic sequence if the…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Q3: (A) Prove that 1. There is no simple group of order 200. 2. Every group of index 2 is normal.

A:

Q: 9) 9 Let I be an ideal of ring R such thut when ever R is Commutakive with identily then so is the…

A: The quotient ring R/I is commutative when (a+I)(b+I) = (b+I)(a+I) for all a+I and b+I belongs to R/I

Q: Given the linear programming problem below where r represents the number of type A items produced…

A: We have to show that if the available number of units of resource 2 is between 60 and 120, the…

Q: (B) Let G be a set of all real numbers except 1. Define on G by a * b = |a|b, where Ja| is the…

A: Let e be the identity element in G (if possible)  Then, for any element a in G,          a*e = e*a =…

Q: t2, 0 2

A: We have to find the Laplace transform of the given function.

Q: Q3: Prove or disprove any four of the following 1.Any abelain group is simple. 2. Any field is a…

A:

Q: 9. Jesse was riding her bicycle and ran over a nail. At this point, a stopwatch starts timing. The…

A: If the height is denoted by a cosine function  h(t)= a cos( bt +c) +d  a is amplitude  2πb  is…

Q: Q31: Define ring. Is every subset of a ring R also a ring?

A: A ring is a nonempty set R equipped with two operations ⊕ and ⊗ (more typically denoted as addition…