Consider the group G = ℚ* × ℤ with operation * on G that can be expressed as: (w, x) * (y, z) = (wy + 1, xz - 1), for all (w, x), (y, z) ∈ ℚ* × ℤ. Find the value of (a, b) in the equation (a, b) = (10, -5)-1 * (9, 4)2

Consider the group G = ℚ* × ℤ with operation * on G that can be expressed as: (w, x) * (y, z) = (wy + 1, xz - 1), for all (w, x), (y, z) ∈ ℚ* × ℤ. Find the value of (a, b) in the equation (a, b) = (10, -5)-1 * (9, 4)2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 20EQ

See similar textbooks

Related questions

Q: A body is launched straight upwards with an initial velocity of 1400 ft/s. what is its velocity at…

Q: (P→ Q) V (Q → P)

Q: Hanna measures 5cm by 4cm on the scale drawing. What are the actual measurements of her kitchen?

Q: 8. Suppose p is false, s is false, r is true. Find the truth value of ~[(s^p) V ~r]

A: See next step for answer

Q: Use any of these formula (an = 1/2 (ª₁ + an ) or an = 7/7 [ 2ª₁ + (n − 1)d ] to solve for the sum of…

A: For across 1. Sum of the first 15 counting numbers Applying the provided formula. It is given by…

Q: 6. 2 dx + (2x - y + 3) dy = 0. Use a change of variable. ANS. y + c = −ln |2x − y + 4). 7. Solve the…

Q: (p→q)↔(~p ✓q) (

Q: Given that = sin evaluated at (x,y)=(5,5) in the box below. Number 4 22 (20+4²+8) c²y f(x,y) Enter a…

A: Find matlab code in next step

Q: . Find the values of the unknowns which satisfy the following equations: a) (sin x, sin 2x, ln e)…

Q: Answer the following questions for the price-demand equation. p+0.005x = 30 (A) Express the demand x…

A: a) x=6000-200p Domain of this function 0≤p≤30 b)E(p)=pp-30 c) E(20)=-2 The demand falls…

Q: H 5. Write down all normalized polynomials of degree at most 4 in Z_2[x]. Underline the reducible…

Q: 2. Select the statement that is the negation of "I'm careful or I make mistakes." A. I'm not careful…

A: Given, The statement is "I`m careful or I make mistakes." We have to find the negation of the given…

Q: Create a 10 simultaneous linear equations with 10 variable unknowns in a, b, c, d, e, f, g, h, j, k…

Q: C): Consider the graph yon ( x₁ = 2, x₁ = 2.4, x₂ = 4) to find the linear interpolation polynomial.

Q: 3. For what values of h is the vector v3 € span {V₁, V₂}, and for which is {V₁, V2, V3} linearly…

Q: (a) Graph both e and its linear approximation on the same plot, displaying a values in the interval…

A: The main objective is to approximate the value of f(x) at x=0.1 by using linear and quadratic…

Q: q^^^ p

Q: 1. Given: (x - 3y) dx + ( 3x + y) = 0 Required: General Solution

A: Given differential equation x-3ydx+3x+ydy=0

Q: The height of a ferris wheel above the ground is modelled by the function h(t) = - 0.5 sin 2t – 3,…

A: Given: h(t) = -0.5 sin 2t - 3 This represents the height of a Ferris wheel above the ground in…

Q: Suppose the marked diagram below conveys information about relationships between pirates, ruffians…

A: Given: The given marked diagram shows the information about the relationships between the pirates,…

Q: For each series, determine whether it converges absolutely, con verges conditionally, or diverges.…

Q: Let the following symbols represent the corresponding statements: s - It is sunny this afternoon. c…

A: The symbols represents the following statements. S: It is sunny this afternoon. c: It is colder than…

Q: ii) Endow R with its order topology. Is it true that if A CR has no minimum and maximum, then the…

Q: Prove that

A: Given parallel lines are l1=n→⋅x=c1..........1 And l2=n→⋅x=c2..........2. Let x1=OA¯ is a point on 1…

Q: Can we use x = vy? (x - y In (y/x)) (vy - y In(y/vy)) --> (vy - y In(1/v))

Q: x(1)? 1) numerically

Q: Let y=e* (Acos(x) + Bsin(x)) be the solution of the initial value problem for the differential…

Q: 47 2 3 2xy 2x Y (x³y²te²x + y sin x) dy = ( 230 ²³+ 2ye² + 2 e ² + 1 ² ( cos x) dx

Q: Which of the following tial equation: is the particular y(3x + 2y) dx - x 2dy = 0 Show your…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

Q: A 50m tape was standardized and was found to be 0.0042m too long than the standard length at an…

Q: y=x-x3/3+x5/15-..... Find ratio test for convergence

A: given series y=x-x33+x515-..... find ratio test for convergence series can be written as…

Q: a) Find all zeros of the polynomial Q(z) = z4 + 1.

Q: n m c) ΣΣ(2m) i=0 j=0

Q: a) A manufacturing company has three factories: A, B and C. The daily output of each is shown below.…

Q: Derive the general solution of the following differential equations: d²y dy i) -1²-x2 + y = f(x)…

A: As per our guidelines ,i can solve only first question 4(i) . kindly repost the 2nd question to get…

Q: Which of the following arguments uses deductive reasoning? A The sum of two integers is an even…

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

Q: b). Fit a Linear regression by considering x as target variable and y as feature X 12 7 Options 8 12…

Q: Solve the equation using the method of simple iteration with an error tolerance & = 0.001? euqation…

A: Given f(x)=-x3+2x2 and f(x)=ex Here -x3+2x2=ex Let g(x)=-x3+2x2-ex For x=0, g(0)=-1x=-1,…

Q: Find the volume of the part in cordinate system section 1(x,y,z>0) which is limited from above to…

Q: Given the rotation matrix R that relates the orientation of bases A and B a B aRb b₂ by b₂ âr 0.9512…

Q: Given the first order nonlinear differential equation: dy 2x dx and the initial condition y(1)=2,…

Q: 13. Show that each conditional statement in Exercise 11 is a tautology using the fact that a…

Q: .45 x 10^8 L/hr x 0.0221 sec = ? dL b. 2.1 x 10^-2 mL/s x 12.00 hr = ?L please show explanation.

A: a. Given 4.45×108 L/hr ×0.0221 sec 4.45×108 L/hr ×0.0221 sec=4.45×108 Lhr ×0.0221 sec=4.45×108 L3600…

Q: Graph the following piecewise functions and discuss continuity: f(x)=√-3x+1, x 2

Q: Determine the differential equation on which the general solution is y=cos (A + Bx). A…

Q: Find the domain of the composition (fog)(x) given f(x)=x²-1 and g(x)=√√x²-4. If possible, find…

A: Given : fx=x2-1 , gx=x2-4 To Find : a Domain of composition (f∘g)x : b Value of f∘g2…

Q: Sketch the surface 1≤z≤ √9-x² - y² 1≤z≤√9-x² - y² and_x² + y² ≤1

A: Given surface 1≤z≤9-x2-y2 and x2+y2≤1

Q: Let A and B be the following matrices: Calculate the matrix A rotates vectors clockwise by a right…

Question

Consider the group G = ℚ* × ℤ with operation * on G that can be expressed as:

(w, x) * (y, z) = (wy + 1, xz - 1), for all (w, x), (y, z) ∈ ℚ* × ℤ.

Find the value of (a, b) in the equation (a, b) = (10, -5)^-1 * (9, 4)².

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find all homomorphic images of the quaternion group.
find the galois group of x^4 + 2x^2 + x + 3 over Q.
The group (Z4 ⨁ Z12)/<(2, 2)> is isomorphic to one of Z8, Z4 ⨁ Z2, orZ2 ⨁ Z2 ⨁ Z2. Determine which one by elimination.
What is the Galois group of x^4-5x^2+6 over ℚ? ℤ_4 V_4 D_4 S_4
Show that the transformation T(x1, x2) = (2x1 − 2x2, 9x1 − 8x2) is invertible, and find a formula for T^−1
G) In 2D transformations, is the following relation TRUE or FALSE? [2] R(9, )R(9, )= R(9, )R(9, ) = R(@, + 4, ).
Let ƒ: R² → R² be an isomorphism where 2 ƒ([-².]) = [-²] and ƒ ([?]) = [1] Find f ¹ ƒ ([^-+^]) X 0 2 I
1.)Integrate: ∫(x+1)(x+2)^6dx Group of answer choices a.)(2/56) (7x + 6)(x + 2)7 + C b.)(2/56) (7x - 6)(x + 2)7 + C c.)(1/56) (7x - 6)(x + 2)7 + C d.)(1/56) (7x + 6)(x + 2)7 + C 2.)Find the derivative of y = log26x. Group of answer choices a.)3.44 b.)1.44 c.)2.44 d.)0.44
The cyclic rule is a sometimes useful identity that applies to the situation in which three variables; x, y, and z are related to one another by a function, z = z(x, y). The rule is: (az/ax)(ax/ay)(ay/əz) = -1 (cyclic rule) Show that the cyclic rule holds for. x² + 2y²+ (1/2)z = 12
Let x belong to a group and |x| = 6. Find |x^2|, |x^3|, |x^4|, and |x^5|. Let y belong to a group and |y|=9. Find |y^i| for i=2, 3, ...,8. Do these examples suggest any relationship between the order of the power of an element and the order of the element?
let G be a group, a,b E G such that bab^-1 =a^r , for some r E N, where N are the natural ones, prove that b^j ab^-j =a^(r^j), for each j E N
Show that PSL(2, Z7) = SL(2, Z7)/Z(SL(2, Z7)), which has order 168,is a simple group.