Please do Exercise 14.4.34 part A and C PROOF. By Proposition 14.4.26 we can writeµ = (a,a,)(a,an-1)-.. (a,a3)(aja2).Now consider first just the last two transpositions in this expression. In theFunctions chapter, we proved the formula (fog) = gof for invertiblefunctions f and g. Since transpositions are invertible functions, we have(laras) (a102) = (a1a2)-"(a1a3)-| = (a1a2)(a1a3)(the second equality follows because every transposition is its own inverse.)If we apply similar reasoning to the last three transpositions in the ex-pression, we find= [(a,a3)(a,a2)](aja4)- = (a,a2)(aja3)(a,a4)Applying this result inductively, we obtain finally:= (a,a2) (a1as) (a1an-1)(a1an),from this expression we may see that a1 + an, an + an-1, an-1+ an-2, - .., a2 +a1, which corresponds to the cycle we want.Because the product of permutations is an associative operation, we mayfind the inverse of any product of cycles by taking the inverses of the cycles inreverse order. (Actually, this is just a special case of the inverse of functioncomposition: (fi o f2 0.. o fn-1° fn)¬ = f o fn0...o f2 o fi.)Example 14.4.32. [(1498)(2468)]- = (2468)-'(1498)-1 = (2864)(1894) =(164)(289).Example 14.4.33. (1357)-2 = [(1357)-)² = (1753)² = (1753)(1753) :(15)(37).%3DExercise 14.4.34. Calculate each of the following.(a) (12537)-1(c) [(1235)(467)]-2(b) [(12)(34)(12)(47)|~|(d) (1254)-(123)(45)(1254)

We have to calculate (a) 12537-1 and (b) 1235467-2

Answered: (a) (12537)-1 (c) [(1235)(467)]-2

Math

Advanced Math

(a) (12537)-1 (c) [(1235)(467)]-2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 44EQ

See similar textbooks

Related questions

Q: Evaluate the double integral: * the dollar signs are integral signs* $$ 20x2y dA over the plane…

A: Given region of integration R enclosed by the lines y=0,y=x and x=1 In the figure red color line…

Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: 1. Let x = 25 – y² be the given curve rotated abou Find the area of the resulting surface (a) Using…

A: Introduction: The formula for the surface area of the curve rotating about the y-axis is given by,…

Q: Un+1(x) – 2xUn (x ) + Un-1(x )– 2U„(x) = 0 -1(x) – 2U,(x ) = 0 (c) Show that (b) can be obtained…

A: From the problem 8b, the given recurrence equation is: Un+1x-2xUnx+Un-1x=0 Differentiate both sides…

Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r2 +y +…

Q: Integrate using Simpson 3/8 Rule with 3 panels from x = 2.0 to 6.0. Solve the relative true error.…

A: "Since you have asked multiple questions, according to guidelines we will solve only the first…

Q: 24, , -6 la"b d) Va

Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

Q: b) Consider the following Linear Programming problem: Min z = 2x, – 3x2 Subject to 1 1 z* +2 54 X1 +…

Q: In the year 2006, the age-adjusted death rate per 100,000 Americans for heart disease was 238.5. In…

A: (a) Let exponential model for the given data will be, Dt=D0e-λt, where Dtis death rate 100,000…

Q: 5. Consider the system of first-order PDES –1 ut + Auz = 0, A = 3 x > 0, t>0 1 (a) Show that the…

A: Given: The system of first order PDEs, ut+Aux=0, where A=5-131, x>0, t>0. Initial conditions:…

Q: provide a formal, deductive proof of the validity of the following: Premises: (A ⇒ B) ⇒ C A ⇒ D ∧ C…

A: F1 : (A -> B) -> C = (~A v B) -> C = ~(~A v B) v C = (A ^ ~B) v C = (A…

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

Q: 2. Supposef(x) = 5ax³ – 6x² – b²x – 7, and g(x) = cx* + 10x³ – (d + 1)x² – 4x + e. Find values for…

A: The given polynomials are fx=5ax3-6x2-b2x-7 and gx=cx4+10x3-d+1x2-4x+e. We have to find the value of…

Q: The function f(x) interval [1, e] at x = Hora lo 0 x is the nat

Q: Students in a fifth-grade class were given an exam. During the next 2 years, the same students were…

A: Given average score of a student after t months is defined by the function ft=91-16logt+1, 0≤t≤24…

Q: Find all eigenvalues and eigenfunctions of the following e X"+ XX = 0, X (0) = X'(2) = 0.

Q: (f) Prove that f(x) = 1.1z + cos(z) has no more than one root. (Note: It is not enough to have…

Q: A non-homogeneous linear differential equation is given. y'' − y' = 2+ex (a) Find the lowest order…

Q: he given matrix equation In Exercises 6 -9, solve Assume that all matrices are invertible. 6. XA² =…

Q: Let T and T' be topologies on a set X such that T' is strictly finer than T. If Y is a subset of X,…

A: Definition: Let Τ and Τ' be topologies on a set X. If Τ' is strictly finer than Τ, then Τ⊂Τ'.…

Q: 4) For a natural number m>1, let P = (0.5)m“ then the sequence P, converges to 0 of order and…

A: By the fact that , if Pn→P, as n→∞ Then, if, limn→∞Pn+1-PPn+1-Pq=λ q= order and λ=Asymptolic error…

Q: Determine the region R in the xy-plane that minimizes the value of (x² + y2 - 4) dA. R={w, vi x + y…

Q: intervals on which f is concave up (down). Then

A: Given, f(x)=5x-3x+6

Q: Assume thatf is differentiable in (-oo, x) and af'(r)N 0 for all a E (-00, 00). Prove that f has the…

Q: Find the solution of the following heat conduction problem using the variable separation method. (0…

Q: The matrix 4 A = -3 7 12 -6 -11 has eigenvalues -5, 1, and 4. Find its eigenvectors. The eigenvalue…

Q: x²+2 dx x+1

Q: Find the eigenvalues A1 < A, and associated orthonormal eigenvectors of the symmetric matrix -5 -5 3…

A: We have to find eigenvalue and orthonormal eign vector.

Q: Given the following differential equation y' + (x + 2)y = 0 After plugging in the appropriate power…

Q: Complete the proof of Property 4 of the following theorem by supplying the justification for each…

A: We have to prove that c0=0 L.H.S=c0 =c(0+0) , ∴ 0+0=0 by additive identity property…

Q: Find the eigenvalues 11 < 12 < 13 and corresponding eigenvectors of the matrix

A: Given, A=-5-201400-130005

Q: Express the solution of the initial value problem y" + 9y = g(t), y(O) = 2, v'(0) = 1 in terms of a…

A: The solution is given below

Q: Approximate the following functions using Taylor series. Solve the absolute and relative error in…

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

Q: Discuss the logical basis for a direct proof and an indirect proof by citing specific logical…

A: To Discuss: The logical basis for a direct proof and an indirect proof by citing specific logical…

Q: If an object's position over time is given by the function d(t) = (t“ + 9)e¯7 for t> 0, on %3D what…

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

Q: general solution (without Laplace Transform): dy dy +2+ 5y = 2e-t. dt dt2

Q: 11 If P(x) 2x* + 6x3 + kx² – 45, find k for which P(-3) = 9.

Q: Exponential Regression The table below shows the value, V, of an investment (in dollars) after n…

A: Given, V: investment (in dollars) after n years n 0 3 7 13 14 19 V(n) 3000 3307.1 3947.8…

Q: Payment of $882 due 1 month ago and $498 due today are to be repaid by a payment of $400 one month…

Q: Find the area of the region that is enclosed by the cardiod r = 6+ 6 sin 0. NOTE: Enter the exact…

Q: Consider the linear system 3 j' = -5 a. Find the eigenvalues and eigenvectors for the coefficient…

Q: (a) Let S {C ): a, 6, c e Z, where 0 denotes the usual integer zero. Given that S is a ring under…

Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

Q: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

Q: Solve and draw l Sketch the graph of the pollowing equations: x² + ag? + z - &x t 124 22 + 35 :0 1.…

A: We know that a function in three variables x, y and z is written as z=fx, y or fx, y, z=0, where x,…

Q: Let E be the 3×3 matrix that corresponds to the row operation R3=R3+R1

Q: Assuming the roles of president and secretary cannot be filled by the same person, how many ways are…

A: When Tyler is chosen as president, we have 3 choices for the post of secretary. So there are 3 such…

Question

Please do Exercise 14.4.34 part A and C

PROOF. By Proposition 14.4.26 we can write
µ = (a,a,)(a,an-1)-.. (a,a3)(aja2).
Now consider first just the last two transpositions in this expression. In the
Functions chapter, we proved the formula (fog) = gof for invertible
functions f and g. Since transpositions are invertible functions, we have
(laras) (a102) = (a1a2)-"(a1a3)-| = (a1a2)(a1a3)
(the second equality follows because every transposition is its own inverse.)
If we apply similar reasoning to the last three transpositions in the ex-
pression, we find
= [(a,a3)(a,a2)](aja4)- = (a,a2)(aja3)(a,a4)
Applying this result inductively, we obtain finally:
= (a,a2) (a1as) (a1an-1)(a1an),
from this expression we may see that a1 + an, an + an-1, an-1+ an-2, - .., a2 +
a1, which corresponds to the cycle we want.
Because the product of permutations is an associative operation, we may
find the inverse of any product of cycles by taking the inverses of the cycles in
reverse order. (Actually, this is just a special case of the inverse of function
composition: (fi o f2 0.. o fn-1° fn)¬ = f o fn0...o f2 o fi.)
Example 14.4.32. [(1498)(2468)]- = (2468)-'(1498)-1 = (2864)(1894) =
(164)(289).
Example 14.4.33. (1357)-2 = [(1357)-)² = (1753)² = (1753)(1753) :
(15)(37).
%3D
Exercise 14.4.34. Calculate each of the following.
(a) (12537)-1
(c) [(1235)(467)]-2
(b) [(12)(34)(12)(47)|~|
(d) (1254)-(123)(45)(1254)

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here