Use the result in Exercise 14 to prove that multiplication by a 2 2 orthogonal matrix

Question:

Use the result in Exercise 14 to prove that multiplication by a 2 × 2 orthogonal matrix is either a rotation or a rotation followed by a reflection about the x-axis.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0471669593

9th edition

Authors: Howard Anton, Chris Rorres

See More Books

Question Posted: Jun 17, 2016 08:08 AM

See More Questions

Use the result in Exercise 15 to determine the condition numbers of the nonsingular square matrices in Exercises 1 and 2. In exercise Show that if A is an n n nonsingular matrix with singular values...
Use the result in Exercise 18 to find the inverses of the following matrices. 0011 0011
Use the result in Exercise 16 to show that if then the solutions of the characteristic equation of A are Use this result to show that A has (a) Two distinct real eigenvalues if (a - d)2 + 4bc > 0 (b)...
In an attempt to identify ecologically friendly methods for controlling mosquito populations, researchers conducted eld experiments in India where aquatic nymphs of the dragony Brachytron pretense...
In the United States currency union, we seem never to worry if a state has a big current account deficit. Have you ever seen such data in the newspaper? Can you even find the data in any U.S....
What are some of the reasons that researchers are interested in finding out the localization of function in the human brain?
Contrast the three types of nonnumeric project selection methods. Could any specific case combine two of them, such as the sacred cow and the operating necessity, or the comparative benefits and the...
The balance in Happ, Inc.'s general ledger Cash account was $12,430 at September 30, before reconciliation. The September 30 balance shown in the bank statement was $11,130. Reconciling items...
The following unadjusted trial balance is for ACE CONSTRUCTION CO. as of the end of its 2017 fiscal year. June 30, 2016, the credit balance of the owners capital account was $59,600, and the owner...
a) Given matrices A, U, E and V, write a pseudocode to determine if UEV is the SVD of A. You may use the function [E, F] = eigs(X) to determine the eigenvectors E corresponding to the eigenvalues in...
What conditions must a and b satisfy for the matrix to be orthogonal? a +b a -b b+a b-a
Prove the equivalence of statements (a) and (c) in Theorem 6.6.1. Theorem 6.6.1 (a) A is orthogonal. (c) The column vectors of A form an orthonormal set in Rn with the Euclidean inner product.
Lisa Walker spent a year in Sierra Leone, West Africa, as a Peace Corps volunteer, and she kept a diary of her experiences. One thing she wrote about was what happened when the government-imposed...
City Feb. Cases March Cases April Cases New York 19 56 189 Los Angeles 6 12 201 Chicago 0 3 14 Houston 19 19 272 Philadelphia 0 1 5 Phoenix 23 78 289 San Antonio 6 9 95 San Diego 3 38 258 Dallas 4 13...
Maximize z = 2x+2y x+6y <30 4x + 2y 32 Subject to I 0 W O 0 Maximum is I = y= at
2. Determine the unknown force. a) Fret 3 N Right b) Fret 10. N Down F-22 N F?5N c) Feet 12 N Up F-28 N d) Fret 10. N Right F? F-12N e) Fret = 0 F-16N E-? F-12N F-15 N F-? F-30 N F-25 N F-32 N F=24N...
If y = ( x ^ 3 + 7 ) ^ x , compute y ' ( 1 ) .
To calculate activity expected duration time, the following parameter is essential? Question 7 options: Distribution time of the unit. Time associated with the failure of the unit. Optimistic or...
What examples can YOU give of the psychological contract between yourself and fellow students; and your university (or faculty/department)?
In Exercises delete part of the domain so that the function that remains is one-to-one. Find the inverse function of the remaining function and give the domain of the inverse function. f(x) = 16x4 -3...
Given the functions 2x and |x|, show that (a) These two vectors are linearly independent in C[- 1, 1]. (b) The vectors are linearly dependent in C[0, 1].
Prove that any finite set of vectors that contains the zero vector must be linearly dependent
Let v1, v2 be two vectors in a vector space V. Show that v1 and v2 are linearly dependent if and only if one of the vectors is a scalar multiple of the other.
XF Ltd. Is an expanding private company in the electric trade. Accounts preparing in January 2019 included the following information: Profit Statement for the year ended 31 st December 2018 Kshs.000...
Check On June 15, 2021, Sanderson Construction entered into a long-term construction contract to build a baseball stadium in Washington D.C., for $340 million. The expected completion date is April...
Q.1 Bassem Company purchased OMR420,000 in merchandise on account during the month of April, and merchandise costing OMR $350,000 was sold on account for OMR 425,000. Required: 1. Prepare journal...

Use the result in Exercise 14 to prove that multiplication by a 2 2 orthogonal matrix

Question:

Step by Step Answer:

Multiplication by the first matrix A in Exercise 24 ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions