Suppose that all the entries in A are integers and det A = 1. Explain why all

Question:

Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A-1 are integers?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:02 PM

See More Questions

Suppose that all the functions in the IS-LM are linear, for example, C(y, T) = C0 + Cy (y - T) I(r) = I0 + Irr L(Y, r) = L0 + Lrr + Lyy Solve for r and y in terms of the parameters G, T, M and C0,...
Let z be the n Ã 1 column vector all of whose entries are equal to 1. (a) Show that if A is an m Ã n matrix, the ith entry of the product v = Az is the ith row sum of A, meaning the sum...
Suppose that a and b are odd integers with a b. Show there is a unique integer c suc that |a - c| = |b - c|.
Consider a static (one-period), closed economy with one representative consumer, one rep- resentative firm, and a government. The level of capital K and government expenditures G in the economy are...
Tompkins Associates reports that the mean clear height for a Class A warehouse in the United States is 22 feet. Suppose clear heights are normally distributed and that the standard deviation is 4...
A project manager discovers that his team has neglected to complete the network diagram for the project. The network diagram is shown in Figure. However, the project manager has some information...
Because both radial readings on the top of a vertical motor are horizontal, how can you differentiate them?
Revenue allocation, bundled products Heavenly Resorts operates a five-star hotel with a world- recognized championship golf course. Heavenly has a decentralized management structure, with three...
Design a rater training program that will help supervisors assess the performance of their subordinates as accurately as possible. What techniques will you include? What important variables can...
According to Franchise Business Review, over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profit of less than...
Show that if A is 2 ( 2, then Theorem 8 gives the same formula for A-1 as that given by Theorem 4 in Section 2.2?
In Exercises 1 - 2, find the area of the parallelogram whose vertices are listed? 1. (0, 0), (5, 2), (6, 4), (11, 6)? 2. (0, 0), (-1, 3), (4, -5), (3, -2)?
What is scalability, in the context of managing a service business?
What kinds of business contract may have an element of wagering incidental to the main purpose of the transaction?
What exception is there to the rule that an agreement is illegal if it purports to indemnify a person against the consequences of his own wrongdoing?
Define the following terms: third party ; assignor ; constructive trust ; beneficiary ; chose in action .
What quality must an insurance contract possess to prevent it from being a wager and therefore void?
How has the privity of contract rule been modified with respect to insurance?
Marc Pty Ltd has accounts receivable of $92 500 at 31 March 2016. An analysis of the accounts shows these amounts: Credit terms are 2/7, n/30. At 31 March 2016 there is a $1600 credit balance in...
The power company must generate 100 kW in order to supply an industrial load with 94 kW through a transmission line with 0.09  resistance. If the load power factor is 0.83 lagging, find the...
Verify that det EA = (det E)(det A), where E is the elementary matrix shown and a = [8 C A = b d
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -6), (1, 3, 5), and (6, 7, 0).
Verify that det EA = (det E)(det A), where E is the elementary matrix shown and a = [8 C A = b d
As of June 30, Year 1, the bank statement showed an ending balance of $16,878. The unadjusted Cash account balance was $15,239. The following information is available: 1. Deposit in transit, $2,190....
Superior Company provided the following data for the year ended December 31 (all raw materials are used in production as direct materials): Selling expenses Purchases of raw materials Direct labor...
Marin Company produces two software products (Cloud-X and Cloud-Y) in two separate departments (A and B). These products are highly regarded network maintenance programs. Cloud-X is used for small...

Suppose that all the entries in A are integers and det A = 1. Explain why all

Question:

Step by Step Answer:

Each cofactor of A is an integer since it is ...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions