1. Prove that x is in W if and only if projw(x) = x. 2. Prove that...

Question:

1. Prove that x is in W if and only if projw(x) = x.
2. Prove that x is orthogonal to W if and only if projw(x) = 0.
3. Prove that projw(projw(x)) = projw(x).

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:21 AM

See More Questions

Let W be a subspace of R n , and let x be a vector in R n . Prove that x is in W if and only if proj W (x) = x.
Let X be a metric space. Prove that X is connected if and only if every nonempty proper subset of X has a nonempty boundary.
Let x, y, z R a) If ||x - z|| < 2 and ||y - z|| < 3, prove that ||x - y|| < 5. b) If ||x|| < 2, ||y|| < 3, and ||z|| < 4, prove that |x y - x z| < 14. c) If ||x - y|| < 2 and ||z|| < 3, prove that...
Do economists have any particular expertise at making normative arguments? In other words, they have expertise at making positive statements (i.e., what will happen) about some economic policy, for...
Robertson Company receives a $64,000, 6-year note bearing interest of 6% (paid annually) from a customer at a time when the discount rate is 8%. What is the present value of the note received by...
What is the half-life of a radioisotope if it decays to 12.5% of its radioactivity in 12 years?
How important is it for a leader to be transformational? Why? Use your experience to support your position. (p. 56)
For 2008, Orchard Corporation reported after-tax net income of $5,800,000. During the year, the number of shares of stock outstanding remained constant at 10,000 of $100 par, 9 percent preferred...
20. What are the characteristics of Fixed Costs and Variable Costs? Know how they move with investment, market expansion decisions
If $6000 is deposited into an account earning simple interest at an annual interest rate of 3% for 5 years, how much interest was earned? A= $ 5600 For the situation in question #1, how much money is...
Let {v1 ( ( ( ( ( v} be an orthogonal basis for and let W = span (v1( ( ( ( ( vn). Is it necessarily true that W = span(vk+1( ( ( ( (vn)? Either prove that it is true or find a counterexample. R"
(a) Prove that (( x ((2 ( ( x ( v1 (2 + ( x ( v2 (2 + ( ( ( + ( x ( vk (2 (This inequality is called Bassel's Inequality.) (b) Prove that Bessel's Inequality is an equality if and only if x is in...
As it is used in the 2nd paragraph (lines 2232), the word party most nearly means: A. A joyous celebration. B. A group of people setting out on a trip. C. A segment of the population. D. A meeting to...
Imagine trying to manage and accommodate the needs of more than 185,000 people at once. Imagine a variety of voices, languages, cultures, ethnic backgrounds, families, lifestyles, ages, and...
Question 1 Case Study Cross-Boundary Teaming for Innovation: Integrating Research on Teams and Knowledge in Organizations In a growing number of cases, teams span organisational boundaries, not just...
Article Assignment Select a business article from a professional news source's business section or professional journal. The article selected is not to be opinion driven. Provide a personal opinion...
Research can be conducted for a variety of reasons including searching for effective change strategies that allow followers to perceive of someone as a leader rather than a manager or studying a...
The revenue recognition principle and the expense recognition principle require that the company recognize related revenue and expense transactions in the same accounting period. Discuss why this...
Write a specification for the function find shown here:
Element compound homogeneous mixture (heterogeneous mixture) 4) A piece of gold has a mass of 49.75 g. What should the volume be if it is pure gold? Gold has a density of 19.3 g/cm (3 points) D=m/v...
Let (a) Show that (b) Prove, by mathematical induction, that cos 0 - sin 0 sin 0 cos O cos 20 - sin 20 A? sin 20 cos 20
Prove Theorem 3.1(a).
Solve the equation for X, given that A = and B = 3X = A - 2B 3 4 -1
44. Dryer Companys policy is to keep 25% of the next month's sales in ending inventory. If Dryer meets its ending inventory policy at the end of April and sales are expected to be 24,000 units in May...
What general conclusions can you draw about your companys liquidity, solvency and productivity based on your ratio calculations. Working Capital 2017 = $9,994 M 2016 = $10,673 M Current Ratio 2017 =...
Tami Tyler opened Tami's Creations, Incorporated, a small manufacturing company, at the beginning of the year. Getting the company through its first quarter of operations placed a considerable strain...

1. Prove that x is in W if and only if projw(x) = x. 2. Prove that...

Question:

Step by Step Answer:

1 2 3 Let ukbe an orthonormal basis for W If Therefore x projw x Then x is in ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions