Question: 3. (5 points) Let U E Rnxn, and suppose Vx E R, |Ual| = ||x||. Prove that U is orthog- onal. Hint: Use the fact

3. (5 points) Let U E Rnxn, and suppose Vx E R", |Ual| = ||x||. Prove that U is orthog- onal. Hint: Use the fact that v . w = - (| |v + w|12 - 1/v - w|12), with v = Ux and w = Uy. Then use the fact that v . w = vw and deduce that UTU = In. Finally, finish the problem with a theorem from class

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Section 8.3 Reading Assignment: Trigonometric Integrals Instructions. Read through this assignment and complete the three exercises below by reading the appropriate passages of the textbook. This...

Question: Over a very long period of time, it has been noted that on Friday's 25% of the customers at the drive-in window at the bank make deposits. What is the probability that it takes 4 customers...

Section 8.3 Reading Assignment: Trigonometric Integrals Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very...

Problem 1 (50 points). Consider two large open economies, Home and Foreign. Each economy is inhabited by a continuum of infinitely lived identical individuals that are grouped into an aggregate risk...

Let A E RNXN, B E RXD be symmetric, positive definite matrices. From the lectures, we can use symmetric positive definite matrices to define a corresponding inner product, as shown below. From the...

>> solve the following please Suppose that you will receive annual payments of $11,000 for a period of 10 years. The first payment will be made 5 years from now. If the interest rate is 5%, what is...

Kindly give only correct answers showing your steps 1. (a) Use the Intermediate Value Theorem to show that the equation - sin (x) + sin(x) =-1 has at least two distinct real solutions on (0, ce)....

- Symbolic functions must be entered using notation similar to the examples given below. - Do NOT include the name of the function or an equal sign. {i.e., do NOT include anything like '1' =' in your...

Section 8.5 Reading Assignment: Integration of Rational Functions by Partial Fractions Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read...

The pathways of carbohydrate metabolism described in Chapters 15 and 16 include two reactions involving the transfer of onecarbon groups. (a) Name the enzymes and the pathways where these reactions...

On January 1, 2019, Anderson Corporation granted 40 million incentive stock options to division managers, each permitting holders to purchase one share of the companys $1 par common shares within the...

22. You are evaluating Woodlawn Racetrack for a potential loan. An examination of the notes to the financial statements indicates restricted cash at year-end amounts to $100,000. Explain how you...

In the 2 0 1 6 Presidential Elections, a large sum of individuals voted for Donald Trump. Many of these individuals voted for the president due to his political promises on issues such as...