(a) Is the set of n x n matrices with det A = 1 a subspace of...

Question:

(a) Is the set of n x n matrices with det A = 1 a subspace of Mn×n?
(b) What about the matrices with det A = 0?

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:29 AM

See More Questions

In Exercises 1-5, assume that A and B are n n matrices with det A = 3 and det B = - 2. Find the indicated determinants. 1. det (AB) 2. det(A2) 3. det(B-1A) 4. det(2A) 5. det(3BT) 6. det(AAT)
Let A and B be n x n matrices. Show that if A is similar to B then there exist n x n matrices S and 7, with S nonsingular, such that A = ST and B = TS
(a) Let K and L be symmetric n x n matrices. Prove that xTKx = xTx for all x Rn if and only if K = L. (b) Find an example of two non-sy mmetric matrices K L such that xTKx = xTLx for all X Rn.
In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 20 citizens are chosen, what is the mean and standard deviation for the number favoring the...
Refer to the previous question. Suppose that the car dealer wanted to find values for A and B that minimized the maximum absolute deviation between the actual and estimated selling price for each...
What is a convertible currency? AppendixLO1
Performance of a bus depot. The performances of public bus depots in India were evaluated and ranked in the International Journal of Engineering Science and Technology (February 2011). A survey was...
Wortham Publishing completed the following transactions for one subscriber during 2014: Oct 1 Sold a one-year subscription, collecting cash of $1,800, plus sales tax of 9%. Nov 15 Remitted (paid) the...
TBS Corporation's budgeted monthly sales are $5,000. 30 percent of its customers pay in the same month and take the 2 percent discount. The remaining 70 percent pay in the month following the sale...
Using the chart of accounts in Figure 2-1, determine the changes to the balance sheet, income statement, job cost ledger, and equipment ledger as the result of billing a client $368,264 for Job 313....
The trace of an n n matrix A Mnn is defined to be the sum of its diagonal entries: tr A = a11 +a22 H+. . . + ann. Prove that the set of trace zero matrices, tr A = 0, is a subspace of Mmn?
Which of the following are vector spaces? Justify your answer! (a) The set of all row vectors of the form (a, 3a). (b) The set of all vectors of the form (a, a + 1). (c) The set of all continuous...
The company received subscriptions for 10,000 shares of $1 par common stock for $30 per share. The company received 30% of the subscription amount immediately and the remainder two months later. Make...
Silver Company makes a product that is very popular as a Mothers Day gift. Thus, peak sales occur in May of each year, as shown in the companys sales budget for the second quarter given below: April...
Among the following statements, select the ones which have a positive environmental impact. Choose several answers Minimising the impact of a product on the environment Avoiding the destruction of a...
Developing Financial Statements: All organizations, including those in the healthcare industry, need to make money to be profitable and survive. Financial statements, such as balance sheets, profit...
The engineers estimated that on average, fuel costs, assuming existing routes and number of flights stay the same, would decrease by almost 18% from an average of 42,000 gallons of jet fuel per...
It's the latest Berkeley trend: raising chickens in a backyard co-op coop. (The chickens cluck with delight at that joke.) It turns out that Berkeley chickens have an unusual property: their weight...
Provide a general description of how hydrometallurgy is used to extract metals from ores.
Imagine you are the HR manager at a company, and a female employee came to you upset because she felt a male coworker was creating a hostile work environment by repeatedly asking her out on dates...
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three-dimensional. Is it possible that A is not diagonalizable? Justify your answer.
Show that if A is both diagonalizable and invertible, then so is A-1.
Show that if A has n linearly independent eigenvectors, then so does AT.
Suppose you bought a bon with an annual coupon rate of 6.5 percent one year ago for $1,032. The bond sells for $1,020 today. a. Assuming a $1,000 face value, what was your total dollar return on this...
During the year 2021, William has a job as an accountant, he earns a salary of $100,000. He has done some cleaning services work on his own (self-employed), where he earned a net income of $50,000....
Fixed cost per unit is $7 when 25,000 units are produced and $5 when 35,000 units are produced. What is the total fixed cost when 30,000 units are produced? Group of answer choices $150,000....

(a) Is the set of n x n matrices with det A = 1 a subspace of...

Question:

Step by Step Answer:

a No The zero matrix is not a...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions