FREE Trial

Let A be a nonsingular n n matrix with n > 1. Show that det(adj A) = (det(A))n-1

Question:

Let A be a nonsingular n × n matrix with n > 1. Show that
det(adj A) = (det(A))n-1

This problem has been solved!


Do you need an answer to a question different from the above? Ask your question!

Step by Step Answer:

Answer rating: 68% (16 reviews)

If det A then det …View the full answer


answer-question
Answered By
tutor-profile-image
Sumit kumar
Education details: QUATERNARY Pursuing M.Tech.(2017-2019) in Electronics and Communication Engg. (VLSI DESIGN) from GNIOT Greater Noida TERTIARY B.Tech. (2012-2016) in Electronics and Communication Engg. from GLBITM Greater Noida SECONDARY Senior Secondary School Examination (Class XII) in 2012 from R.S.S.Inter College, Noida ELEMENTARY Secondary School Examination (Class X) in 2010 from New R.J.C. Public School ,Noida CERTIFICATION Summer Training in ‘WIRELESS EMBEDDED SYSTEM’ from ‘XIONEE’ for the six weeks. EMBEDDED SYSTEM Certificate issued by CETPA INFOTECH for one day workshop. Certificate of Faculty development program on OPTICAL COMMUNICATION and NETWORKS for one week.
5.00+ 1+ Reviews 10+ Question Solved
Related Book For  answer-question
Linear Algebra with Applications

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books
View Solution
Create a free account to access the answer
Cannot find your solution?
Post a FREE question now and get an answer within minutes. * Average response time.
Question Posted: June 13, 2016 00:48:47
See More Questions

Students also viewed these Linear Algebra questions

Q:
Let A be a nonsingular n n matrix. Use mathematical induction to prove that Am is nonsingular and (Am)-1 = (A-1)m for m = 1, 2, 3, ...
A:
For m 1 A 1 1 A 1 A 1 1 Assume the result holds in......
Q:
Let A be a nonsingular n n matrix and let B be an n r matrix. Show that the reduced row echelon form of (A|B) is (I|C), where C = A-1B.
A:
Since A is nonsingular it is row equivalent to I Hence the......
Q:
Let A be a nonsingular n n matrix and let be an eigenvalue of A. (a) Show that 0. (b) Show that 1/ is an eigenvalue of A-1.
A:
a det A 1 2 n If A is nonsingular then det A 0 and hence all......
Q:
If the firm's lowest average cost is $52 and the corresponding average variable cost is $26, what does it pay a perfectly competitive firm to do if? a. The market price is $51 b. The price is $36 c....
A:
a When the market price is 51 the firm should lower the output in producing the......
Q:
If the dollar begins trading at $1.30 per euro, with the same interest rates given in Problem 3, and the ECB raises interest rates so that the rate on euro deposits rises by 1 percentage point, what...
A:
1 287 per euro Since the exchange rate is quoted as per e......
Q:
While on vacation, Janet traveled the full length of Interstate Highway 5 from the U.S.- Canadian border to the U.S. Mexican border (see the map below). She recorded the following travel times...
A:
a b......
Q:
Fair White Limited is a FMCG company largely catering to domestic markets. During the year 201617, it received its maiden export order for $ 2 million for supply of fairness cream to USA. The order...
A:
Profit and loss statement for the year 201617 Sales will be recorded u......
Q:
Gibson Motors manufactures specialty tractors. It has two divisions: a Tractor Division and a Tire Division. The Tractor Division can use the tires produced by the Tire Division. The market price per...
A:
Req 1 Lowest Variable cost of 18 17 1 High......
Q:
Design and write, in pseudocode, a dynamic programming algorithm that solves the following problem. Input: A sequence S of positive integers, and its length n Output: The subsequence S' of largest...
A:
this code is working fine and time complexcity is O n......
Q:
At t = 0 a sealed test tube containing a chemical is immersed in a liquid bath. The initial temperature of the chemical in the test tube is 80 F. The liquid bath has a controlled temperature...
A:
a The initial temperature of the bath is T m 0 60 so in the short term the temperature of t......
Q:
Suppose that Q is a matrix with the property Q-1 = QT. Show that qij = Qij / det(Q)
A:
The j i entry of Q T i......
Q:
det(A + B) = det(A) + det(B) In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. In each of...
A:
The statement is false......
Q:
Rework Exercise 9.4 using the standardized CUSUM parameters of h = 8.01 and k = 0.25. Compare the results with those obtained previously in Exercise 9.4. What can you say about the theoretical...
A:
To standardize There are no out of control signals What......
Q:
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many...
A:
Convert the rate of increase in the radius of the Moon s orbit from centimeters per year to meters p......
Q:
How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of on Earth)?
A:
The height an astronaut can jump on the Moon compared to Earth can be calculated using the concept o......
Q:
On March 26, 2012, Dale M. Smith deposited a cashiers check drawn from Chase Bank in the amount of $294,500.99 to his account at The State Bank. The next day, Smith requested State Bank to wire...
A:
Based on the provided information it appears that the cashier s check deposited by Dale M Smith at T......
Q:
An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of 0.150 m/s 2 as it goes through. The station is 210 m long. (a) How long did the...
A:
To solve this problem we can use the equations of motion specifically those for uniformly decelerating motion The four key equations of motion for thi......
Q:
An infant's pulse rate is measured to be 130 5 beats/min. What is the percent uncertainty in this measurement?
A:
To find the percent uncertainty in the measurement of an infant s pulse rate y......
Q:
Are the following sets of vectors linearly independent? Show the details of your work. [1 2 3 4], [2 3 4 5], [3 4 5 6]. 4 5 6 7]
A:
No It is remarkab......
Q:
Answer the following two independent questions. a. MM Corporation is considering several proposed investments for the coming budget year. MM produces electrical apparatus for industrial complexes....
A:
SOLUTION a To calculate the weighted average cost of capital WACC for the MM project proposal we need to calculate the cost of equity and the cost of......
Q:
Does there exist a 3 à 3 symmetric matrix with eigenvalues λ1 = -1, λ2 = 3, λ3 = 7 and corresponding eigenvectors If so, find such a matrix; if not,...
A:
Yes The given vectors are pair wise orthogonal so we consider the equation P 1 AP D or A P......
Q:
Show that if 0 has no eigenvalues and consequently no eigenvectors. s cose
A:
The characteristic equation of A is 2......
Q:
Find the eigenvalues of the matrix C1 C2. Cn A= C1 2 Cn
A:
Call the matrix A and show that A 2 c 1 c 2 c n A tr A A Thus A k tr A k1 A for k 2......
X-UMEUS Agility Ladder Speed Training Equipment Set-20ft Agility Ladder 12 Soccer Cones 4 Hurdles - ISBN: B0BRMYJW1V - Free Book