Let be an eigenvalue of A with associated eigenvector x. Show that + r is

Question:

Let λ be an eigenvalue of A with associated eigenvector x. Show that λ + r is an eigenvalue of A + rln with associated eigenvector x. Thus, adding a scalar multiple of the identity matrix to A merely shifts the eigenvalues by the scalar multiple?

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 07:47 AM

See More Questions

Let be an eigenvalue of a stochastic matrix A (see section 3.7). Prove that | | 1.
Let where B and C are square matrices. (a) If Î» is an eigenvalue of B with eigenvector x = (x1,..., xk)T, show that Î» is also an eigenvalue of A with eigenvector = (x1,...,...
Let be an eigenvalue of a linear operator T: V V. Prove that the eigenvectors of T corresponding to are the nonzero vectors in the kernel of I - T.
Starting on January 1, 2024, you put $125 every month into an account with an APR of 4.10%. Your last payment is on December 1, 2032. On January 1 of that year, the balance in the account, rounded to...
1. Develop a CPM/PERT network for Moore House Contractors and determine the probability that the contractors can complete a house within 45 days. Does it appear that the Moores might need to increase...
For each of the following, determine c so that the function can serve as the probability distribution of a random variable with the given range: (a) f(x) = cx for x = 1, 2, 3, 4, 5; (b) (c) f(x) = cx...
A fluid flows past a sphere with an upstream velocity of $V_{0}=40 \mathrm{~m} / \mathrm{s}$ as shown in Fig. P4.46. From a more advanced theory it is found that the speed of the fluid along the...
The following describes a purchasing process at Ludlow Winter Sports, Inc., a manufacturer of skis, snowshoes, and other winter recreational gear. The description here is limited to the process for...
Describe the advantages and disadvantages of the three temporal orientations - past, present, and future. How do these temporal perspectives differ across culture?
Describe a new business for which you think a virtual organizationwhich has no physical office or headquarters could be an effective design. What are some ways that the organization could use IT to...
Let A be an n ( n matrix with eigenvalues 1 and 2, where 1 ( 2. Let S1 and S2 be the eigenspaces associated with 1, and 2, respectively. Explain why the zero vector is the only vector that is in both...
Let A and B be n ( n matrices such that Ax = x and Bx = (x. Show that (a) (A + B)x = ( + ()x? (b) (AB)x = (()x?
a. Use a graphing utility to produce a graph of the given function. Experiment with different windows to see how the graph changes on different scales. Sketch an accurate graph by hand after using...
The following information relates to La Greca Co. for the year 2019. Instructions After analyzing the data, prepare an income statement and a retained earnings statement for the year ending December...
What is the average power of the triangular wave shown in Fig. 1.90? Average power $P=\frac{1}{3} \mathrm{~W}$. Figure 1.90 Triangular wave 1 0 x(t) 1 M 3 4 2 5 6 t
Toth Company had the following assets and liabilities on the dates indicated. Toth began business on January 1, 2018, with an investment of $100,000 from stockholders. Instructions From an analysis...
Lei Company accumulates the following adjustment data at December 31. 1. Services performed but unbilled total $1,000. 2. Supplies of $300 have been used. 3. Utility expenses of $225 are unpaid. 4....
The ledger of Herrera, Inc. on March 31, 2019, includes the following selected accounts before adjusting entries. An analysis of the accounts shows the following. 1. Insurance expires at the rate of...
For the following exercises, evaluate the common logarithmic expression without using a calculator. 2 log(100 3 )
Choose two matrices A and B with dimension 2 x 2. Calculate det A, det B, and det (AB). Repeat this process until you are able to discover how these three determinants are related. Summarize your...
Find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
Find a polynomial function of degree 5 with - 12 as a zero of multiplicity 2, 0 as a zero of multiplicity 1, and 1 as a zero of multiplicity 2?
Suppose that a polynomial function of degree 4 with rational coefficient has the given numbers as zeros Find the other zero(s)? a. - 1, (3, 11/3 b. - (2, - 1, 4/5 c. - i, 2 - (5
Have a brief introduction, discussion of the topics/points, and a conclusion.what you have learned during the course( Organizational Dynamics and Effectiveness).Their relevance to your career....
Using the article provided below, you are required to analyse the company information to define the business goals and evaluate whether the supply chain is a strategic fit with the business and...
Create output that shows a scatterplot with a line of best fit for your data. Explain what a line of best fit is? Submit both the output file (SPSS) as well as your Word summary.

Let be an eigenvalue of A with associated eigenvector x. Show that + r is

Question:

Step by Step Answer:

If Ax x then for any scala...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions