Use mathematical induction to show that if A is an eigenvalue of an n x n matrix

Question:

Use mathematical induction to show that if A is an eigenvalue of an n x n matrix A, with x a corresponding eigenvector, then, for each positive integer m, λm is an eigenvalue of Am, with x a corresponding eigenvector.

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 12:09 PM

See More Questions

Use mathematical induction to show that if f(x) = xex, then f (n) (x) = (x + n) ex.
Use mathematical induction to show that if n is a positive integers, the sequence 2 mod n, 22 mod n, 222 mod n, 2222 modn, . . . is eventually constant (that is, all terms after a finite number of...
Use mathematical induction to show that if Q Rnm is both upper triangular and orthogonal, then qj = ej j = 1,..., n.
If you wanted to double $1,000 in 10 years' time, what average rate of return would you require on your investment?
Compute P20, P47, P83, Q1, Q2, and Q3 for the following data. 4501 4487 2936 7341 8908 1152 7422 9914 8776 3021 0825 2360
On treatment with phenylhydrazine, aldohexoses A and B give the same osazone. On treatment with warm nitric acid, A gives an optically inactive aldaric acid, but sugar B gives an optically active...
Table 2.1 lists the history of 940 wafers in a semiconductor manufacturing process. Suppose that 1 wafer is selected at random. Let $H$ denote the event that the wafer contains high levels of...
The report clearly needs to be redesigned. Design a report (or reports) that better suits Stephen Links. What approach can the analyst take in suggesting more reports with a less-crowded format?...
Produce a high level project plan for the design, implementation, commissioning of the data centre. References - Schneider Electric - Data Centre Projects, Schneider Electric, Schneider Electric -...
Refer to the schedule of cost of goods manufactured prepared for Huron Corporation in the preceding problem. Required: 1. How much of the manufacturing costs incurred during 20x2 remained associated...
Suppose x is an eigenvector of A corresponding to an eigenvalue . a. Show that x is an eigenvector of 51 - A. What is the corresponding eigenvalue? b. Show that x is an eigenvector of 51 - 3A + A2....
If p(f) = c0 + c1t + c2t2 +... + Cn1n, define p(A) to be the matrix formed by replacing each power of t in p(t) by the corresponding power of A (with A0 = 1). That is,
What questions must be answered when designing products?
State whether or not each of the following events would result in a liability being recognised in the accounts at 30 June. If so, what will the liability be called? If not, explain the reasons why it...
MNO Ltd purchased a one-year insurance policy on 1 April. The entire premium of $6000 was recorded by debiting prepayments. Year-end is 30 June. 1. Give the 30 June adjusting entry. 2. What amount...
1. In a recent annual report the following information is provided: Assume this amount all related to insurance and that $70 million cash was paid during the year to the insurance company. What is...
Now that you are a famous businessperson, you are frequently asked to make after-dinner speeches on business topics. Without thinking about it too much, you agreed to make a speech on accrual...
The balance sheet of ABC Ltd as at 31 December 2015 and the cash receipts and payments for the year ended 31 December 2016 are shown below. Additional information: a. As at 31 December 2016, the...
The receiving department employs one worker who spends 25% of his time on the receiving activity and 75% of his time on inspecting products. His salary is $40,000. The amount of cost assigned to the...
Kenneth Hubbard has prepared the following list of statements about managerial accounting and financial accounting. 1. Financial accounting focuses on providing information to internal users. 2....
The shift transformation, S.({yk}) = {yk-1}, shifts each entry in the signal one position to the right. The moving average transformation, creates a new signal by averaging two consecutive terms in...
The shift transformation, S.({yk}) = {yk-1}, shifts each entry in the signal one position to the right. The moving average transformation, creates a new signal by averaging two consecutive terms in...
a. Let A be a diagonalizable n n matrix. Show that if the multiplicity of an eigenvalue is n, then A = I. b. Use part (a) to show that the matrix is not diagonalizable. A = 2 1 0 0 2 1 0 0 2
Question 5 In 50 words or more, explain how advertising is implemented through each type of media listed below. Advertising Media Types How Advertising is Implemented Through Each Type of Media i....
1. Research and outline the Lean Method and how it applies to marketing a products. Explain in one fifty words. 2. Outline your understanding of market research and what is should include: Be...
MUN Faculty of Business Administration | Managing Social Enterprises: Marketing Ultimate project goal Write a letter that appeals to me (or your audience), and convinces them to take a key action, or...

Use mathematical induction to show that if A is an eigenvalue of an n x n matrix

Question:

Step by Step Answer:

Assume that Ax x for some nonzero vector x The desir...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions