Let 1, 2,....., k be distinct eigenvalues of an n ( n matrix A with associated eigenvectors

Question:

Let λ1, λ2,....., λk be distinct eigenvalues of an n ( n matrix A with associated eigenvectors x1, x2 ..... xk. Prove that x1, x2, ..... , xk are linearly independent?

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:50 AM

See More Questions

Let and be distinct eigenvalues of a Hermitian matrix A. (a) Prove that if x is an eigenvector corresponding to and y an eigenvector corresponding to , then x*Ay = x*y and x* Ay = x* y. (b) Prove...
Let A be a symmetric matrix (that is, A = AT) with distinct eigenvalues Î»1 and Î»2. For such a matrix, if v1 and v2 are eigenvectors belonging to the distinct eigenvalues...
Let A = [ jk ] be an n x n matrix with (not necessarily distinct) eigenvalues 1 , , n . Show. kA has the eigenvalues k 1 , , k n . A m (m = 1, 2, ) has the eigenvalues 1 m , , n m . The...
Define change management and its significance in organizations. Discuss the challenges faced during the process of organizational change and strategies to overcome resistance.
The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it...
Markus Companys common stock sold for $2.75 per share at the end of this year. The company paid a common stock dividend of $0.55 per share this year. It also provided the following data excerpts from...
Explain why it is important to report communicable diseases, adverse drug reactions, and infectious diseases.
A major city in the northeast wants to establish a central transportation station from which visitors can ride buses to four historic landmarks. The city is arranged in a grid, or block, structure...
If I threw a 1 . 0 kg text book up into the air with a speed of 5 . 0 km / s , what maximum height would it reach? The mass of the Earth is 5 . 9 8 x 1 0 ^ 2 4 kg and its radius is 6 . 3 8 1 0 ^ 6...
On January 1. Ruiz Company issued bonds as follows: Face Value: Number of Years: Stated Interest Rate: Interest payments per year 500,000 15 7% Required: 1) Calculate the bond selling price given the...
Show that if A is nonsingular and diagonalizable, then A-1 is diagonalizable?
Show that if a matrix A is similar to a diagonal matrix D, then Tr(A) = Tr(D), where Tr(A) is the trace of A?
The human resources department at a large multinational corporation wants to be able to predict average salary for a given number of years of experience. Data on salary (in $1000s) and years of...
5. Who performed the first experiments that proved the physical existence of antibodies? A) Tiselius and Kabat B) Paul Ehrlich and Jules Bordet C) Tizzoni and Cattani D) Von Behring and Kitasato 6....
9. Which immunoglobulin has the heaviest chains? A) IgE B) IgG C) IgM D) IgA 10. What is the shape of an immunoglobulin molecule? A) 'Y' or 'T' B) Circle C) Line D) Square 11. What are the two types...
13. What holds the two heavy chains of an immunoglobulin together? A) Hydrophobic bonds B) Salt linkages C) Disulfide bonds D) Hydrogen bonds 14. What is the term for the monovalent fragment with...
17. Which class of immunoglobulin contains mu heavy chains? A) IgA B) IgE C) IgM D) IgG 18. Which class of immunoglobulin contains gamma heavy chains? A) IgE B) IgM C) IgG D) IgA 19. Which class of...
25. Can all immunoglobulins be considered antibodies? A) Yes B) Only some C) No D) It is unclear 26. Which immunoglobulin plays a major role in conferring protectionagainst microbial pathogens? A)...
Distinguish between authorized stock and issued stock. Why might the number of shares issued be more than the number of shares outstanding?
If |62x|>9, which of the following is a possible value of x? A. 2 B. 1 C. 0 D. 4 E. 7
Is it possible for the graph of a polynomial function to have no y-intercept? no x-intercepts? Explain your answer?
Explain why values of a function must be all positive or all negative between consecutive zeros?
In synthetic division, why is the degree of the quotient 1 less than that of the dividend?
1. Mention five key organizational characteristics that the Cll research team identified for organizations with effective quality management systems. provide brief discussion of each and how it...
When a metal was exposed to photons at a frequency of 1.46 1015 s1, electrons were emitted with a maximum kinetic energy 3.60 10-19 J. G ? Calculate the work function, , of this metal. J/photon What...
No. 101 Debit Cash $ 2,400 Question 2 (10 pts) On November 1, 2024, the account balances of Schilling Equipment Repair were as follows. Accumulated Depreciation-Equipment A Clipboard Font Alignment...

Let 1, 2,....., k be distinct eigenvalues of an n ( n matrix A with associated eigenvectors

Question:

Step by Step Answer:

First observe the difference between this result and Theorem 75 Theorem 75 shows that if all the eig...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions