(a)Prove that an orthogonal 2 ( 2 matrix must have the form Where Is a unit vector....
Question:
Where
Is a unit vector.
(b)Using part (a), show that every orthogonal 2 ( 2 matrix is of the form
Where 0 ( ( ( 2 (.
Transcribed Image Text:
or cos θ sin θ -sin θ cos θ | cos θ sin θ or cos θ | -cos θ R2 R2
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (10 reviews)
a Suppose that is an orthogonal matrix Then So a 2 b 2 1 and c 2 d 2 1 and thus both columns of Q ar...View the full answer
Answered By
Shebla K
I am an MBA graduate having experience as an Assistant Professor at University level for two years. I always prepare well for a class as I believe that only if you become an ocean you can give a bucket of water. Being a teacher was not only my profession but also my passion.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
(a) Prove that an orthogonal 2 Ã 2 matrix must have the form where is a unit vector. (b) Using part (a), show that every orthogonal 2 Ã 2 matrix is of the form where 0 ¤ u...
-
Use Exercise 28 to determine whether the given orthogonal matrix represents a rotation or a reflection. If it is a rotation, give the angle of rotation; if it is a reflection, give the line of...
-
Use Exercise 28 to determine whether the given orthogonal matrix represents a rotation or a reflection. If it is a rotation, give the angle of rotation; if it is a reflection, give the line of...
-
According to Dr. Grant, creatives are people who ________. A. Are procrastinators B. Act on multiple ideas C. Plan out each detail D. Are highly confident with no doubts about their success
-
Using a financial calculator, provide a solution to each of the following situations. (a) Tina Deboer owes a debt of $42,000 from the purchase of her new sport utility vehicle. The debt bears annual...
-
Two employees are talking about ethics in their workplaces. Jay says that ethics training and codes of ethical conduct are worthless; Maura says they are the only ways to ensure ethical behavior by...
-
Some believe that the top three ratios that every technology company needs to understand and track are the quick ratio, debt to equity ratio, and gross profit margin. Describe each of these ratios...
-
Clark Kent earns $800 per week for a five-day week, and he is entitled to 12 paid holidays and four weeks of paid vacation. a. Over how many weeks should the holiday pay and vacation pay be expensed?...
-
Assessment in the Transition Process. Objective: To explore, examine and discover the process and types of assessments supporting transition programs and services. a. click on this link to review...
-
A ride hailing company has their DB structured in 3 major tables as described in the SCHEMA section below. Write a query to fetch the top 100 users who traveled the most distance using the service....
-
Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in. If ( is the angle between x and y, prove that the angle between Qx and Qy is also (. (This proves that the linear transformations...
-
Let A and B be n ( n orthogonal matrices. (a)Prove that A (AT + BT)B = A + B. (b)Use part (a) to prove that, if det A + det B = 0, then A + B is not invertible.
-
A copper tube with a circular cross-section has a length L =1.25 m, thickness t = 2 mm, and shear modulus of elasticity G = 45 GPa. The bar is de signed to carry a 300 N ? m torque acting at the...
-
A free-floating exchange rate system uses global supply and demand to set exchange rates. True or False
-
A local content requirement is one kind of government rule meant to a. reduce foreign exports. b. limit imports. c. tax foreign goods. d. subsidize domestic producers.
-
A mini-multinational is a company that a. is small but still does international sales. b. is a large international firm. c. is a small local business. d. is now illegal because of trade barriers.
-
Are there any possible alternatives to consider? What other decision could you make so that each side (domestic and international) benefits?
-
Do the benefits of offshore outsourcing outweigh the costs? Why or why not?
-
Using data collected by zoologist Reto Zach, the work done by a crow to break open a whelk (large marine snail) can be estimated by the function where H is the height (in meters) of the whelk when it...
-
What is an insurable interest? Why is it important?
-
The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational...
-
Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...
-
Apply Jacobis method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each...
-
Should an MNC purchase Nestl stock yes or no? Recommendations should include the company's sustainability plans, the image of the company, Gordon Growth result, and financial performance. Any...
-
Can the sponsor, or general partner, continue to achieve such high returns? Framed another way, can the general partner earn a 25+% return on the $6,305,000 received at the end of the 10th year? If...
-
Select a hospital that publicly displays their financial performance on their website. Describe the Profit Loss Statement: Review top revenue items Review cost comparison compared to previous year...
Study smarter with the SolutionInn App