Prove that (ai + a2 +....... + an)2 n(a21 + a22 + .......+ a2n) for any

Question:

Prove that
(ai + a2 +....... + an)2 ≤ n(a21 + a22 + .......+ a2n) for any real numbers a\..........a". When does equality hold?

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:37 AM

See More Questions

Let A1, A2, and A3 be events, and let Bi represent either Ai or its complement Ai. Then there are eight possible choices for the triple (B1, B2, B3). Prove that the events A1, A2, A3 are independent...
If G = (V, E) is an undirected graph with |V|-n and |E| = k, the following matrices are used to represent G. Let V = {v1, v2, . . . , Define the adjacency matrix A = (aI j)nÃn where aIJ = 1 if...
Use the following matrices, where all elements are real numbers, to show that each statement is true for 2 2 matrices. (c + d)A = cA + dA, for any real numbers c and d. ) ] b11 b12 [b21 b2] C11...
Describe the risk assessment approach used for Enterprise Risk Management(ERM) at Worker's Compensation Fund(WCF). How does this approach compare to ISO 31000? Does it consider risks with upside...
Barbs Beach Bar operates seven days per week. Barb uses only full-time employees and wants each employee to have two consecutive days off each week. She believes that she needs a minimum of three...
Ficus Tree Farm issued five $1,000 bonds with a stated annual interest rate of 12 percent on January 1, 1997, that mature on January 1, 2002. Interest is paid semiannually on June 30 and December 31....
Sociology fieldwork methods. Refer to University of New Mexico professor Jane Hoods study of the fieldwork methods used by qualitative sociologists, presented in Exercise 2.195 (p. 136). Recall that...
Engineering design is an activity that is vital to the success of any motor vehicle manufacturer. Identify the level at which engineering design would be classified in the cost hierarchy used with...
What formula to use to find Payback Period and NPV? (in Excel) A B D E F G H NLO 00 1 Exhibit 1 2 2021 Capital Expenditure Requests 3 4 Request Number Manager ID Initial Investment 5 21000001 10736...
Delaney Products, Inc. provided the following information from its current- year trial balance. Delaney issued $ 55,000 of common stock on October 1 of the current year. The company also repurchased...
Use the Cauchy-Schwarz inequality to prove (a cos + b sin )2 a2 + b2 for any 9,a,b.
The Law of Cosines: Prove that the formula ||v - w||2 = ||v||2 + ||w||2 - 2 ||v|| ||w|| cos, (3.21) where is the angle between v and w, is valid in any inner product space.
Which of the following alternatives to the underlined portion would NOT be acceptable? A. NO CHANGE B. Other countries C. Other countries D. Other countries,
PART 1: DIGITAL TECHNOLOGY: Describe the key digital technology groups studied in this course and include a discussion of two examples for each group. PART 2: SOCIAL MEDIA: As studied in this course,...
Doing a strategic analysis of GraceKennedy Limited, What is the current level of its economic performance, an indication of the factors responsible for the current performance and recommendations for...
Dynamic capability is the ability for change and manage corporate learning. It allows an enterprise to adapt, develop and respond to future opportunities and discontinuous technologies. Innovation...
What potential solutions can organizations try to help support the adoption of a CDSS? In other words, what are some ways an organization can address the factors of implementation obstruction that...
Identify and briefly describe and discuss the three most important factors in building and maintaining trust among virtual global team members. Include in your discussion how you can leverage these...
(A) A handbook lists the aqueous solubility of AgOCN as 7 mg/100 mL at 20 C. What is the K sp of AgOCN at 20 C? (B) A handbook lists the aqueous solubility of lithium phosphate at 18 C as 0.034 g Li...
Repeat the previous problem, but close the positions on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify...
For each of the matrices in Exercise 2: (a) Determine the rank. (b) Find the closest (with respect to the Frobenius norm) matrix of rank 1. Exercise 2 (a) (b) (c) 2 2 1300 0120 2000
The matrix has singular value decomposition Use the singular value decomposition to find orthonormal bases for R(A) and N(AT). 4004 5335 2662 1-3 2-3 2-3 2-3 2-3 1-3 0600 2000
Prove that, if A is a symmetric matrix with eigenvalues 1, 2,..., n, then the singular values of A are |1|, |2|,..., |n|.
Question 3 (24 marks) Wonderful Technology Company Limited sells computers and accessories. Data of the store's operations are as follow: Sales are budgeted at $400,000 for December 2019, $420,000...
Kratz Manufacturing Company uses an activity-based costing system. It has the following manufacturing activity areas, related cost drivers and cost allocation rates: Activity Cost Driver Cost...
You are a Partner with Fix-It Consultants and have been engaged in an advisory capacity with a software company, called MoveFast. The company is seeing a sharp decline in revenue, with the primary...

Prove that (ai + a2 +....... + an)2 n(a21 + a22 + .......+ a2n) for any

Question:

Step by Step Answer:

Set v a 1 a n T w 1 1 1 T so that Cau...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions