Let V be an inner product space. Show that if w is orthogonal to each of the

Question:

Let V be an inner product space. Show that if w is orthogonal to each of the vectors u1,u2, ... ,ur, then it is orthogonal to every vector in span (u1, u2,..., ur,}.

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: 978-0471669593

9th edition

Authors: Howard Anton, Chris Rorres

See More Books

Question Posted: Jun 17, 2016 08:07 AM

See More Questions

Let V be an inner product space. Show that if u and v are orthogonal unit vectors in V, then ||u - v|| = 2.
Let V be an inner product space and v V a fixed element. Prove that the set of all vectors w V that are orthogonal to v forms a subspace of V.
Let V be an inner product space. If u and v are vectors in V, Show that (u, v) = ||u + v||2 -1/4 ||u-v||2
A small project consists of three activities: A, B, and C. To start activity C, both activities A and B need to be complete. Activity A takes 3 days with a probability of 50 percent and 5 days with a...
The Green Hornet sells earnings forecasts for international securities. Its credit terms are 2/10, net 30. Based on experience, 55 percent of all customers will take the discount. The firm sells...
An electric utility is planning its annual project of shutting down one of its steam boilers for maintenance and repair. An analysis of this project has identified the following principal activities...
Water flows in a rectangular channel with a flowrate per unit width of $q=1.5 \mathrm{~m}^{2} / \mathrm{s}$ and a depth of $0.5 \mathrm{~m}$ at section (1). The head loss between sections (1) and...
For each of the following fund types, indicate its fund category by placing either GF for governmental funds, PF for proprietary funds, or FF for fiduciary funds in the space provided before each...
The Danville city council is evaluating the casino project and its impact. Will this be a good sustainable project for the city and have good results? The council looked at the impact of casinos on...
? On January 1, 20X2, Page Company acquired 70% of the outstanding common shares of Sage Ltd. for $45,500 in cash. On that date, Sage had $20,000 in common shares outstanding and $20,000 in retained...
Let A be the matrix in Exercise 16. Find bases for the column space of A and nullspace of AT
Let {w1, w2,..., wk} be a basis for a subspace W of V. Show that W consists of all vectors in V that are orthogonal to every basis vector.
What is the relationship between the processing time at a resource and its capacity? a. They are the same. b. They are reciprocals of each other. c. They are multiples of each other. d. They are not...
To what extent do contemporary theories of intersectionality provide a comprehensive framework for understanding the complex interrelationships between race, gender, class, sexuality, and other axes...
Rewrite the following code using a Select Case Block. (10 marks) If num = 1 Then } 1stOutput.Items.Add("lambs") ElseIf num = 2 Or num = 3 Then 1 1st Output.Items.Add("chicken") ElseIf num >= 4 And num
1. How can YOU be exceptional when applying for a job? 2. What is the secret in a "Purple Cow" job-seeking technique? Explain. Do you know any of your classmates who are like this? Explain. 3. When...
How does globalization influence cultural homogenization and heterogenization, and what are the socio-economic and political ramifications of these processes on local communities and national...
A firm issues a floater with 100 face value paying LIBOR on the first day of each calendar quarter. The floater will mature on Jan 1, 2040. Assume the yield curve is always flat. The floater was...
Does a geometric sum always have a finite value?
Assume you are the accountant for Catalina Industries. John Catalina, the owner of the company, is in a hurry to receive the financial statements for the year ended December 31, 20X1, and asks you...
Let where all four blocks are n Ã n matrices. (a) If A11 and A22 are nonsingular, show that A must also be nonsingular and that A-1 must be of the form (b) Determine C. A11 A12 O A22
Let A and B be n Ã n matrices and let M be a block matrix of the form Use condition (b) of Theorem 1.4.2 to show that if either A or B is singular, then M must be singular. A C M = O B B
Let A and B be n Ã n matrices and define 2n Ã 2n matrices S and M by Determine the block form of S-1 and use it to compute the block form of the product S-1MS. AB O
Select a company you are familiar with and detail one short-term and one longer-term strategy, then discuss how the role of human resource development can provide valuable advice and counsel in the...
Sunspot Beverages, Limited, of Fiji uses the weighted-average method of process costing. It makes blended tropical fruit drinks in two stages. Fruit juices are extracted from fresh fruits and then...
How does TPM intersect with Lean Manufacturing principles? Discuss the synergies between TPM and Lean practices, such as continuous improvement (Kaizen) and value stream mapping, in reducing waste...

Let V be an inner product space. Show that if w is orthogonal to each of the

Question:

Step by Step Answer:

By definition u is in span u 1 u 2 u ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions