Rotation of vectors in R3 about an axis is a linear map. Show that linear maps do

Question:

Rotation of vectors in R3 about an axis is a linear map. Show that linear maps do not commute by showing geometrically that rotations do not commute.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:04 AM

See More Questions

Describe the set of vectors in R3 orthogonal to the one with entires 1, 3, and -1.
Follow the directions of Exercise 18. (a) T: R3 R3 is the reflection about the yz-plane. (b) T: R3 R3 is the orthogonal projection on the xz-plane. (c) T: R3 R3 is the dilation by a factor of 2....
Example 1.9 shows how to represent rotation of all vectors in the plane through an angle about the origin, with respect to the standard bases. (a) Rotation of all vectors in three-space through an...
Write a reflective paper about Disability Network West Michigan
Draw a supply curve for turkey. In your diagram, show a price of turkey and the producer surplus at that price. Explain in words what this producer surplus measures.
The average amount of water used per day by a person living in Ethiopia, Eritrea, Djibouti, Gambia, Somalia, Mali, Mozambique, Tanzania, or Uganda, is the same as someone in a developed country: a....
3. Can you think of any major changes in recent years that have resulted without a scandal or crisis of some sort?
At December 31, 2016, Shutdown Manufacturing Limited had outstanding a $300,000, 12% note payable to Thornton National Bank. Dated January 1, 2014, the note was issued at par and due on December 31,...
At year-end 2024, a zero coupon bond maturing on December 31, 2026 has a yield of 6%; a similar zero coupon bond maturing a year later has a yield of 6.5%. Based on the expectations hypothesis of...
Part 1 Even after the recent public experiment about cereal box weights, Consumers Concerned About Cereal Cheaters (CCACC) remains convinced that Oxford Cereals has misled the public. The group has...
We can ask how the matrix product operation interacts with the transpose operation. (a) Show that (GH)T = HTGT. (b) A square matrix is symmetric if each i, j entry equals the j, i entry, that is, if...
In the proof of Theorem 2.12 we used some maps. What are the domains and codomains? Theorem 2.12 If F, G, and H are matrices, and the matrix products are defined, then the product is associative...
May Patt is the controller for Patt Industries. She has been asked to develop a plan for installing a management information system in her company. The president has already approved the concept and...
8. [1.5 pts] We want to design a plastic bottle. It will have inner diameter d1 and outer diameter d2 so that the thickness becomes t=(d2-d1)/2. The inner diameter is determined as 10 cm. The...
The perimeter of the rectangle below is 106 units. Find the value of y. 3y+3 2y | y-0
1 . Ameya made 4 0 % of investment in personal business, 2 0 % in stocks and the rest in mutual funds. There are 2 0 % , 1 0 % and 1 5 % of chances in obtaining profit in personal business, stocks...
4. We are given the following joint distribution over the random variables A, B, C, and D. Please answer the following questions. Show the necessary tables. You can (and should) share computations...
(f) It is hypothesized that for t> 400 s the relation between t and h is of the form where k and n are constants. h=kt (i) Outline how, using a graphical technique, you would verify this hypothesis.
Let n be a nonzero integer. Find a domain on which (x) = (1 x n ) 1/n coincides with its inverse. The answer depends on whether n is even or odd.
For the following exercises, find the area of the triangle. Round to the nearest hundredth. 22 50 36
Consider the linear DEs in Problem with y(0) = 1 (a) Use a computer package with different numerical methods to find y(1) (b) Use the exact solution (as found in the corresponding problem to computer...
The direction fields of three DEs are shown in Fig. 2.2.3. (a) Label the equations linear or nonlinear. Of the two that are linear, which is homogeneous and which is non homogeneous? (b) Explain...
From your conclusions in Problem, decide which of the direction fields in Fig. 2.2.4 represent linear homogeneous equations. Explain your reasons in each case (A) (B) (D) (E) )
Selected comparative financial statement data for DAS inc. Balance Sheet (En milliers de dollars) 2017 2018 Assets Assets CT - Cash 41.63 47.5 - Accounts Receivable 64.2 72.6 - inventories 969.7...
please help!! One chance at turning in!!! 16 rows! I'd highly appreicate it I am unsure what information you need... I provided all Current Attempt in Progress Mike Greenberg opened Grouper Window...
Blue Ridge Marketing Inc. manufactures two products, A and B . Presently, the company uses a single plantwide factory overhead rate for allocating overhead to products. However, management is...

Rotation of vectors in R3 about an axis is a linear map. Show that linear maps do

Question:

Step by Step Answer:

Consider r x r y R 3 R 3 rotating all vectors 2 radians counterclockwise about the x and y axe...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions