Question: (a) Show that the linear transformation defined by a 3 Ã 3 proper orthogonal matrix corresponds to rotating through an angle around a line through

(a) Show that the linear transformation defined by a 3 Ã— 3 proper orthogonal matrix corresponds to rotating through an angle around a line through the origin in R3-the axis of the rotation.
(b) Find the axis and angle of rotation of the orthogonal matrix

4-5 3 3-6

Step by Step Solution

★★★★★

3.46 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The axis of the rotation is the eigenvector v correspo... 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 (2623).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

A linear transformation L: V W is said to map V onto W if L(V) = W. Show that the linear transformation L defined by L(x) = (x1.x1 +x2,x1 +.x2 + x3)T maps R3 onto R3.

In each case, show that the linear transformation T satisfies T2 = T. (a) T: R2 R2; T(x, y) = (x + y, 0) a+e b+d a +e b+d

Let T: M22 M22 be the linear transformation defined by (a) Which, if any, of the following matrices are in ker( T)? (i) (ii) (iii) (b) Which, if any, of the matrices in part (a) are in range(T)? 3 2...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

A spherical satellite is ying through space while spinning on its axis. Unfortunately the gyroscope on the satellite is broken, and so the usual measurements for the axis and angular velocity of...

All the information are in it (i) g(x) = x?(x + 5)%(x 1)(x 4) (a) Degree: ; Leading coefficient: ; based on this the end behavior is: (b) the x-intercepts: X-intercept Multiplicity Bounce or cross?...

please help to answer these 8 questions, thank you~ Question 1. In each of the following, determine if the given set is a subspace of R2 or not. For each case in which the set is a subspace, verify...

MA1200 A2 F23 Assignment 7 Name: Total Marks: 20 Due Nov 7 1. Recall that Q_1:I1R2 > R2, reflection in the line y : a) [2 marks] Find MQ_1 and use this matrix to find Q_1(x) wherex : (2, 3). b) [4]...

I need help Overview As we are seeing, linear algebra comes up in a lot of applications. One of the prime applications for vectors and matrix transformations is the area of computer graphics and the...

In an IE Matrix, do you believe it is more advantageous for a division to be located in quadrant II or IV? Why?

Youre an analyst in the finance department of Flyover Corp., a new firm in a profitable but risky high-tech business. Several growth opportunities have come along recently, but the company doesnt...

Based strictly on liquidity, which of the following assets should not be included in a client's emergency fund? Question 3 options: The cash value of a life insurance policy. 3 month Treasury bills....

What is the basis for trade? What advantages are there to specialisation?

Let X be a random variable with range [1, 1] and let fX (x) be the density function of X. Find (X) and 2(X) if, for |x|

Let X be a random variable with density function fX. Show, using elementary calculus, that the function Ф(a) = E((X a)2) takes its minimum value when a = (X), and in that case (a) = 2(X).

Let X, Y, and Z be independent random variables, each with mean and variance 2. (a) Find the expected value and variance of S = X + Y + Z. (b) Find the expected value and variance of A = (1/3) (X + Y...

there are 3 approaches to solve this. Future Value isnt one of them. any help on what the 3 approaches are? i also need it be solved in excel. Problems in Business Finance 382, Test 1, Q12, Fall 2009...

Calculate the Present Value of Growth Opportunities ( PVGO ) Medtronic is expected to earn $ 8 . 0 2 next year. The company has a discount rate of 1 3 % and is able to reinvest its earnings at an ROE...

The balance sheet for Pie Crust, Inc., is shown here in market value terms. There are 29,000 shares of stock outstanding. Market Value Balance Sheet Cash $156,000 Fixed assets 560,010 Equity $716,010...