(a) Show that if A has size n n, then det(A) = (1) n detA. (b)...

Question:

(a) Show that if A has size n × n, then det(−A) = (−1)ⁿ detA.

(b) Prove that, for n odd, any n × n skew-symmetric matrix A = −A^T is singular.

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: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

See More Books

Question Posted: Apr 15, 2023 07:01 AM

See More Questions

A matrix A is said to be skew symmetric if AT = -A. For example, is skew symmetric since If A is an n Ã n skew symmetric matrix and n is odd, show that A must be singular 0.
Prove the following statements or provide counterexamples to show they are not true. a. The product of two symmetric matrices is symmetric. b. The inverse of a nonsingular symmetric matrix is a...
If the random variable T is the time to failure of a commercial product and the values of its probability density and distribution function at time t are f(t) and F(t), then its failure rate at time...
What types of costs are associated with a Stance" sock vending machine located in an airport? At Cleveland Hopkins International Airport in northeastern Ohio, a vending machine that dispenses socks...
Ripley Lumber Company purchased $240,000 of equipment on September 1, 2016. Required a. Compute the amount of depreciation expense that is deductible under MACRS for 2016 and 2017, assuming that the...
Jones Jr. and his wife, Mary, store their household goods at his parents home while they are looking for an apartment. A fire at the parents home damages $3000 worth of their property. Assuming the...
A consumer testing service is commissioned to rank the top 3 brands of laundry detergent. Ten brands are to be included in the study. a. In how many different ways can the consumer testing service...
An analyst was asked to predict the gross social benefits of building a public swimming pool in Dryville, which has a population of 70,230 people and a median household income of $31,500. The analyst...
BAK Corp. is considering purchasing one of two new diagnostic machines. Either machine would make it possible for the company to bid on jobs that it currently isn't equipped to do. Estimates...
Go back and quickly review the rules that the Sarbanes-Oxley Act of 2002 placed on the auditing profession as described in this chapter. What do you think are the two or three main purposes of these...
Prove that if A is an invertible matrix, then AA T and A T A are also invertible.
An alternative solution strategy, also called GaussJordan in some texts, is, once a pivot is in position, to use elementary row operations of type #1 to eliminate all entries both above and below it,...
If a firm files for bankruptcy under Chapter 11 of the bankruptcy code, which party gets the first opportunity to propose a plan for the firms reorganization?
A program X running on processor A has a global CPI of 2 and a clock frequency of 2 GHz. The same program X running on processor B has a global CPI of 5 and a clock frequency of 5 GHz. what processor...
20 cm Room (3) 20 cm + 1 D=10 cm + 20 cm [ 10 10 cm Figure 7 (d) Using configuration factor formulae given in Figures 7(a), 7(b) and 7(c) Calculate configuration factor F12 in Figure 7(d) treating...
2. Let P(3,2,1),Q(2,1,c) and R(c,1,0) be points in R3. (a) Use the cross product definition to find the area of triangle PQR in terms of c. (b) For what values of c (if any) is PQR a right triangle?
Find and classify the discontinuities of the following function as removable or nonremovable. If a classification has no discontinuities, write None for your answer. Answer 03023 Hawks Learning A(x)=...
Do you see a parallel between the evolution of goals in economics and the move from Corporate Social Responsibility (CSR) to environmental, social, and governance (ESG), ? If so, please explain...
In year 1, GSL Corp.s alternative minimum tax base was $2,000,000 and its regular tax liability is $350,000. a. What is GSLs total tax liability for years 1, 2, 3, and 4 (by year) assuming the...
Convert the numeral to a HinduArabic numeral. A94 12
Classify the following matrices as (i) Regular (ii) Nonsingular, and/or (iii) Singular: (a) (b) (c) (d) 4 2 145 242 312 312 241 ]23 02-5 3163 3021 1132
For each of the following linear systems find a permuted L U factorization of the coefficient matrix and then use it to solve the system by Forward and Back Substitution. (a) 4x1 - 4x2 + 2x3 = 1 -3x1...
(a) Explain why and are all legitimate permuted LU factorizations of the same matrix. List the elementary row operations that are being used in each case. (b) Use each of the factorizations to solve...
help!!! Use the above information to calculate ending inventory using FIFO for a company that uses a perpetua/inventory system
Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361 outlets in the United States, Canada, United Arab Emirates, Japan, South Korea and Saudi Arabia. If...
The market price of a semi-annual pay bond is $979.86. It has 21.00 years to maturity and a yield to maturity of 7.34%. What is the coupon rate? Submit Answer format: Percentage Round to: 0 decimal...

(a) Show that if A has size n n, then det(A) = (1) n detA. (b)...

Question:

Step by Step Answer:

a To show that if A has size n n then detA 1n detA we can use the properties ...View the full answer

Applied Linear Algebra

Students also viewed these Mathematics questions