Use the properties det(AB) = det(A) det(B) and det(I n ) = 1 for n x
Question:
Use the properties det(AB) = det(A) • det(B) and det(In) = 1 for n x n matrices to show the following:
a. Then x n matrices with determinant 1 form a normal subgroup of GL(n, R).
b. Then x n matrices with determinant ±1 form a normal subgroup of GL(n, R).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (3 reviews)
a Let H be the subset of GLn R consisting of the n n matrices with determinant 1 The property ...View the full answer
Answered By
David Muchemi
I am a professional academic writer with considerable experience in writing business and economic related papers. I have been writing for my clients who reach out to me personally after being recommended to me by satisfied clients.
I have the English language prowess, no grammatical and spelling errors can be found in my work. I double-check for such mistakes before submitting my papers.
I deliver finished work within the stipulated time and without fail. I am a good researcher on any topic especially those perceived to be tough.
I am ready to work on your papers and ensure you receive the highest quality you are looking for. Please hire me to offer my readily available quality service.
Best regards,
4.60+
27+ Reviews
61+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
For n X n matrices A and B, and n 1 column matrices C, D, and X, solve each matrix equation in Problem for X. Assume that all necessary inverses exist. AX - X = C
-
For n X n matrices A and B, and n 1 column matrices C, D, and X, solve each matrix equation in Problem for X. Assume that all necessary inverses exist. AX + C = BX + D
-
For n x n matrices A and B, and n x 1 column matrices C, D, and X, solve each matrix equation in Problem for X. Assume that all necessary inverses exist. AX + X = C
-
The pressure at the bottom of a swimming pool is evenly distributed. Suppose we look at a cast iron plate of 7272 kg lying on the ground with an area of 100 m2. What is the average pressure below...
-
How are U.S. GAAP and IFRS changing over time?
-
Your company has been asked to provide advice to the Australian Government on a number of proposals it has received from the (fictional) Australian Civil Engineers Union (ACEU)*. The ACEU is...
-
How do managers use CVP analysis to make decisions?
-
Based on Problem 2-9A, prepare a statement of owners equity for Jay Pembroke for the month of April 20--.
-
Discussion questions: With reference to the reading explain what Wolf means by a sane deep self. Do you think that Jojo is morally responsible (viz., deserving of praise and blame for his actions)?...
-
A bank manager wishes to provide prompt service for customers at the banks drive- up window. The bank currently can serve up to 10 customers per 15- minute period without significant delay. The...
-
Let N be a normal subgroup of G and let H be any subgroup of G. Let HN = { hn | h H, n N}. Show that H N is a subgroup of G, and is the smallest subgroup containing both N and H.
-
Give an example of a nontrivial homomorphism for the given groups, if an example exists. If no such homomorphism exists, explain why that is so. : Z x Z 2Z
-
You and a friend decide to spend $100 each on concert tickets. Each of you alternatively could have spent the $100 to purchase a textbook, a meal at a highly rated local restaurant, or several...
-
Define the Security Market Line (SML), and briefly describe the difference between the Security Market Line (SML) and the Capital Market Line (CML). Describe how the CAPM can be tested empirically,...
-
discuss the ethical and socio-economic dimensions of biodiversity conservation, including issues related to environmental justice, indigenous rights, and sustainable resource management?
-
Why/when do you think it might be important to calculate mass discharges rather than just referring to concentrations in a wastewater discharge? This subject title is " Industrial Wastewater...
-
hat methodologies and metrics are employed in quantifying biodiversity, considering taxonomic, genetic, and functional dimensions, and how do these measurements inform conservation strategies?
-
Moana and Jane are employed by Sobecal (a pharmaceutical company) to research and develop new pharmaceuticals. Moana and Jane are full of enthusiasm for research, so at weekends they often carry out...
-
By means of an example, show that A j F, j 1, need not imply that j=1 Aj F, and similarly for j=1 Aj.
-
Create an appropriate display of the navel data collected in Exercise 25 of Section 3.1. Discuss any special properties of this distribution. Exercise 25 The navel ratio is defined to be a persons...
-
Use methods of longitudinal data analysis to compare the rates of change in serum creatinine over time by treatment group?
-
Compare your results with those obtained using ordinary ANOVA methods based on slopes in Problem 12.49?
-
Assess the crude association between MI and OC use without taking age into account (provide a two-tailed p-value)? Cardiovascular Disease Refer to Table 13.7. Table 13.7 Association between MI and OC...
-
The Metrobank offers one year loans of $1,000,000 each with a stated rate of 9%, charges a % loan origination fee, imposes a 10% compensating balance requirement, and must hold a 6% reserve...
-
Expectations regarding environmental oversight, reporting, and performance will continue to rise. Over the past several years, investors have increasingly focused on portfolio companies'...
-
SALINA, Kansas (AP) --Police officers and the city of Salina have been dismissed from a lawsuit filed by a woman interrogated last year about photos printed at a Wal-Mart store that included...
Study smarter with the SolutionInn App