Question: Compute both compositions F G and G F of the following affine functions on R2. Which pairs commute? (a) F = counterclockwise rotation

Compute both compositions F ○ G and G ○ F of the following affine functions on R2. Which pairs commute?
(a) F = counterclockwise rotation around the origin by 45°; G = translation in the y direction by 3 units.
(b) F = counterclockwise rotation around the point (1, 1)T by 30°; G = counterclockwise rotation around the point (-2, l)T by 90°.
(c) F = reflection through the line y = x + 1; G = rotation around (1, 1)T by 180°.

Step by Step Solution

★★★★★

3.54 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a is counterclockwise rotation around the point by 45 o is counterclockwise ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2498).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Compute the first and second derivatives of the following function. l +e

Compute the first and second derivatives of the following function. p(x)=iter

Compute the first and second derivatives of the following function. g(x) = ex / x.

1. A translation can be defined as moving a figure to a new location with no change to the size or shape of the figure? True Fals e 2 points QUESTION 2 1. The following is an example of a...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

(1) Using the matrices and vectors below, solve for the following quantities. For any matrix-vector multiplica- tion, show your response as a linear combination using vector equations. If an...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

Which of the following terms best describes the relationship between a corporation and the CPA it hires to audit corporate books? Employer and employee. Employer and independent contractor. Master...

Pruitt Corporation acquired all of the voting stock of Soto Corporation on January 1, 2010, for $210,000 when Soto had common stock of $150,000 and retained earnings of $24,000. The excess of implied...

most employees who continue working after retirement age must do so because of financial instability. true or fals

Use the following diagram of the market for cigarettes to answer the following questions. a According to the diagram, how much is the government tax on cigarettes? b What price do producers receive...

Consider the Izod impact test described in Exercise 8-23. Compute a 99% tolerance interval on the impact strength of PVC pipe that has confidence level 90%. Compare the length of the tolerance...

Compute a 99% tolerance interval on the brightness of the television tubes in Exercise 8-24 that has confidence level 95%. Compare the length of the prediction interval with the length of the 99% CI...

Consider the margarine test described in Exercise 8-25. Compute a 99% tolerance interval on the polyunsaturated fatty acid in this particular type of margarine that has confidence level 95%. Compare...

Workshop Exercise Variance Analysis Barack Obama Ltd manufactures a single product, Tuxedos. The company uses a standard cost accounting system. From notes scattered on the desk of the cost...

Please show your works and answer in Finance way (not in excel) and highlight the answer. thank you 8. (Corporate application) You own a gold mine that is running dry. It will generate $2 mil in cash...

You've borrowed $28,512 on margin to buy shares in Ixnay, which is now selling at $43.2 per share. You invest 1,320 shares. Your account starts at the initial margin requirement of 50%. The...