(a) Show that if A = A-1, then det(A) = 1. (b) If AT = A-1, what...

Question:

(a) Show that if A = A-1, then det(A) = ±1.
(b) If AT = A-1, what is det(A)?

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: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:01 AM

See More Questions

(a) Show that if a > 0, then 1/a > 0 and 1/(1/a) = a. (b) Show that if a < b, then a < 1/2 (a + b) < b.
a. Show that if A is any positive number, then the sequence defined by xn = 1/2xn1 + A/2xn1, for n 1, converges toA whenever x0 > 0. b. What happens if x0 < 0?
(a) Give an example to show that if A can be partitioned as where P, Q, R, and S are all square, then it is not necessarily true that det A = (det P) (det S) - (det Q) (det R) (b) Assume that A is...
The instruction to convert 'A' to 'a' is: Select one: a. or al, 0000010b b. or al, 00100000b or al, 00100100b d. or al, 00010000b e. or al, 01100000b
What is the purpose of conducting break-even analysis?
An investment offers a total return of 13.5 percent over the coming year. Powell Arms thinks the total real return on this investment will be only 8.6 percent. What does Powell believe the inflation...
With Figure 1.5 in mind, how could changes in government policies affect accounting activities? All Stakeholders Financial statements Bank & agency reports Accounting System Tax returns Management &...
Gillman Co. is forecasting sales of 62,000 units of product for August. To make one unit of finished product, 5 pounds of raw materials are required. Actual beginning and desired ending inventories...
What is the price of a 5% fixed rate coupon bond, $100 par value, which has 8 years to maturity given a market discount rate of 5.353%?
A presently owned machine can last 3 more years, if properly maintained at a cost of $15,000 per year. Its AOC is $31,000 per year. After 3 years, it can be sold for an estimated $9000. A replacement...
Show that if A is a matrix such that in each row and in each column one and only one element is not equal to 0, then det(A) ( 0.
Show that if A and B are square matrices, then det = (det A)(det B). 8
In Problems 6184, solve each equation on the interval 0 < 2. 4(1 + sin0) cos0
Talk about bond investor and give 2 specific financial ratios that creditors or investors would be most interested in when analyzing financial statements, and why?
ABC Company Ltd has 1.4 million shares common valued atTshs200 per share =Tshs280 million. Debt has face value ofTshs50 million and trades at 93% of face (Tshs46.5 million) in the market. Total...
The company wrote off a customer's account because that company went bankrupt. The accounts receivable was for $ 9 , 5 0 0 . How would be enter as a journal entry?
Accounting is the backbone of any business, serving as the systematic process of recording, summarizing, and analyzing financial transactions. In the realm of accounting businesses, the need for...
Customers X and Y each bought the homes you and Z had sold (see Problem 1).Each home costs 200.Like you, X bought with 25% down. Like Z, Y bought all cash, not financing anything. Unfortunately for...
A company is considering two alternative machines with different net cash flows and salvage values. Present value amounts are calculated using Excel and the results follow. a. Compute the net present...
Suppose you are comparing just two means. Among the possible statistics you could use is the difference in means, the MAD, or the max min (the difference between the largest mean and the smallest...
In each part, find ker(T), and determine whether the linear transformation T is one-to-one. (a) T: R2 R2, where T(x, y) = (y, x) (b) T: R2 R2, where T(x, y) = (x + y, x - y) (c) T: R2 R3, where...
Let T1: P2 P3 and T2: P3 P3 be the linear transformations given by the formulas T1(p(x)) = xp(x) and T2(p(x)) = p(x + 1) Find formulas for T1-l (p(x)), T2-1 (p(x)), and (T2 o T1)-1 (p(x))
In each part, determine whether the linear operator T: M22 M22 is one-to-one. If so, find (a) (b) :/HE. :*) -ca
Prepare a short report for David on the financial analysis completed. Your report should include: The results of your analysis Your recommendation based on the required rate of return, if the...
Michelle is a 47-year old woman who has not been to see any healthcare provider since the birth of her third child 6 years ago. She is considering making an appointment to discuss medical options for...
The starting salaries of recent graduates and their majors in college were surveyed. Specifically, 300 graduates were included in the survey. You conduct a test to determine whether majors and...

(a) Show that if A = A-1, then det(A) = 1. (b) If AT = A-1, what...

Question:

Step by Step Answer:

a By Corollary 33 detA 1 1 de...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions