Let A be an eigenvalue of an invertible matrix A. Show that A-1 is an eigenvalue of

Question:

Let A be an eigenvalue of an invertible matrix A. Show that A-1 is an eigenvalue of λ-1.

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 12:05 PM

See More Questions

Let A be an n x n matrix and let A be an eigenvalue of A whose eigenspace has dimension k. where I where I is the k x k identity mairk. (b) Use Theorem 6.1.1 to show that is an eigenaIue of A with...
Let A be an eigenvalue of the n ( n matrix A. Prove that the subset of Rn (Cn) consisting of the zero vector and all eigenvectors of A associated with . is a subspace of Rn (Cn). This subspace is...
Let A be an invertible matrix and let 1 and n be the eigenvalues with the largest and smallest absolute values, respectively. Show that cond (A) |1| / |n|
Estimate the cash value of a life insurance policy as of December 31, 2016 based on the following information: Cash value as of January 2016 $90,000 Total premium during the year $ 8,000 Term life...
Determine the mean, the variance, and the standard deviation of the following discrete distribution. x P(x) 1 ...........238 2 ...........290 3 ...........177 4 ...........158 5 ...........137
D. Carson and F. Leggatt formed a partnership on June 1 to operate a shoe store. Carson contributed $50,000 cash and Leggatt contributed $50,000 worth of shoe inventory. During the month of June, the...
What are the main objectives of an international compensation plan? Would an integrated solution or a best-of-breed solution make more sense for a large manufacturing corporation? Do you believe that...
Garnett Jackson, the founder and CEO of Tech Tune-Ups, stared out the window as he finished his customary peanut butter and jelly sandwich, contemplating the dilemma currently facing his firm. Tech...
Case: The rise of ad blockers has begun to make a dent in the advertising revenue earned by content creators and providers. Ad blockers identify and eliminate content based on its IP address,...
Wood Limited, a newly established manufacturing company in the Southern Industrial area, manufactures two types of Boardroom Tables. One type of these Boardroom tables is sold locally and the other...
Construct an example of a 2 2 matrix with only one distinct eigenvalue.
Show that if A2 is the zero matrix, then the only eigenvalue of is 0.
If salaries payable was $75,000 at the beginning of the year and $40,000 at the end of the year, should $35,000 be added to or deducted from income to determine the amount of cash flows from...
How do you allocate fixed and variable costs to each transaction and to each customer? Are there formal written guidelines, and do you handle these issues consistently across your firm?
Compare and contrast the five major conflict styles.
Various library resources and websites contain the text of famous speeches. Find one with excerpts or the entire speech of someone famous who interests you. Watch the speech and evaluate according to...
Describe the administrative duties leaders are expected to perform, and explain how leaders can perform these effectively.
List and explain six factors involved in leading group discussions.
Calculate the missing value for Problem. Initial value Final value Percent change ? $300 50
A simple random sample of 220 university students were asked what pasta they usually order and with which sauce. The preferences of these respondents are summarised below: Sauce Bolognese Pasta...
A denotes an m x n matrix. Justify each answer. (T/F) The column space of A is the range of the mapping x Ax.
Justify each answer (T/F) A subspace is also a vector space.
Justify each answer. (T/F) In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix.
You are a supervisor at your company. You've overheard Employee A making offensive comments to other employees, and Employee B has complained about these comments. You've given Employee A a verbal...
What is the probability of developing and dying from cancer today?
On January 1, 2024, Majestic Mantles leased a lathe from Equipment Leasing under a finance lease. Lease payments are made annually. Title does not transfer to the lessee and there is no purchase...

Let A be an eigenvalue of an invertible matrix A. Show that A-1 is an eigenvalue of

Question:

Step by Step Answer:

If is an eigenvalue of A then there is a nonzero ...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions