Suppose A is a 3 x 3 orthogonal matrix with det(A) = 1. Given that the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose A is a 3 x 3 orthogonal matrix with det(A) = 1. Given that the eigenvalues of a real matrix occur in conjugate pairs, show that A must have an eigenvalue equal to 1. Moreover, if ||u|| = 1 with Au= u, and u, v, w an orthonormal basis for R³, show that in these basis, A must be of the form: 10 0 A=0 cos 0 -sin 0 0 sin cos Suppose A is a 3 x 3 orthogonal matrix with det(A) = 1. Given that the eigenvalues of a real matrix occur in conjugate pairs, show that A must have an eigenvalue equal to 1. Moreover, if ||u|| = 1 with Au= u, and u, v, w an orthonormal basis for R³, show that in these basis, A must be of the form: 10 0 A=0 cos 0 -sin 0 0 sin cos
Expert Answer:
Answer rating: 100% (QA)
CS Solution of Given A be the orthogonal matrixie AAtI Then ... View the full answer
Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
Posted Date:
Students also viewed these accounting questions
-
A is a 3 x 3 matrix with two eigenvalues. Each eigenspace is one-dimensional. Is A diagonalizable? Why?
-
Suppose A is a 3 x 2 matrix and B is 3 x 3 matrix. If A, B both represent linear transformations, which of the following linear transformations are defined? O AB OBA A OB None of these
-
Prove that the eigenvalues of an upper triangular (or lower triangular) matrix are its diagonal entries.
-
For the increasing marginal-extraction-cost model of the allocation of a depletable resource, how would the ultimate cumulative amount taken out of the ground be affected by (a) An increase in the...
-
A partial list of Frend Hotels costs is provided below. a. Champagne for guests. b. Cost to mail a customer survey. c. Training for hotel restaurant servers. d. Cost to replace lobby furniture. e....
-
Use RIA Checkpoint Citator 2nd to evaluate Deluxe Check Printers, Inc., 15 Cl. Ct. 175. a. Which tax years were in question in the case? How was the case treated upon appeal? What is the citation of...
-
Raymonde, the owner of a small company, asked Holmes, public accountant, to conduct an audit of the company's records. Raymonde told Holmes that an audit is to be completed in time to submit audited...
-
Tri-State Bank and Trust is considering giving Josef Company a loan. Before doing so, management decides that further discussions with Josefs accountant may be desirable. One area of particular...
-
Please help QUESTION #5 Galaxydoughs Tea Lid. has been considering a special investment for some time. The project will require an immediate capital expenditure of $1 million for required equipment....
-
The Antwerp Lions play in the Flemish Football League. The Lions play in the Antwerp Stadium (owned and managed by the City of Antwerp), which has a capacity of 30 000 seats (10 000 lower-tier seats...
-
Please help me figure this out. I need help with problems 11-18 the picture of the income statement and balance sheet is supposed to help find the total to each one on this excel sheet. P lease Do...
-
Describe the processes of gene regulation at the transcriptional, post-transcriptional, and epigenetic levels, highlighting the roles of transcription factors, non-coding RNAs, and chromatin...
-
Given the circuit below, find the total resistance (in ohms), the total current (in amps), and the current (in amps) through R3. Report the resistance answer to two significant figures and the...
-
The Coca-Cola Company recently reported dividends per share of U.S. $1.60 and a dividend yield of 3.04%. PepsiCo Inc. reported dividends per share of U.S. $3.82 and a dividend yield of 2.85% for the...
-
Brian (46) and Liz (36) aren't sure about how they are saving for their children Lily (7), Ellie (4) and Lincoln (18 months) Brian is a professor at UIC and Liz stays at home with children. They both...
-
V Find the equivalent resistance. (+ 1 www 12 4. 1 109 8
-
peer review/reflection of : This week's reading of "Television, Disordered Eating, and Young Women in Fiji" by Anne Becker, tells us how a study back in 1998 was conducted through narrative data...
-
Why do bars offer free peanuts?
-
In R3 the shear in the xy-direction with factor k is the linear transformation that moves each point (x, y, z) parallel to the x-plane to the new position (x + ky, y + kz, z)- (See the accompanying...
-
Use the method of Example 4 to find all sixth roots of 1.
-
Find a basis for the subspace of R4 spanned by the given vectors. (1, 1, - 4, - 3), (2, 0, 2, -2), (2, - 1, 3, 2)
-
Question: Sports Graphics, Inc. imports "Chill" brand coolers from Taiwan. Chill coolers have an outer shell of vinyl, with handles and pockets, and an inner layer of insulation. In a recent lawsuit,...
-
Question: In a recent WTO case, several nations claimed that American laws concerning shrimp fishing were unfair and illegal. The case demonstrated a conflict between two important values. What were...
-
Question: Flyby Knight (FK) contracts to sell 12 helicopters to Air Nigeria, for $8 million each. Payment is to be made by letter of credit, issued by the Bank of Nigeria, confirmed by Citibank in...
Study smarter with the SolutionInn App