Question: (a) Show that if A has size n n, then det(A) = (1) n detA. (b) Prove that, for n odd, any n

(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 = −AT is singular. 

(c) Find a nonsingular skew-symmetric matrix.

Step by Step Solution

★★★★★

3.50 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

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

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Applied Linear Algebra Questions!

Q:

A matrix A is said to be skew symmetric if AT = -A. For example, is skew symmetric since If A is an n à n skew symmetric matrix and n is odd, show that A must be singular 0.

Q:

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...

Q:

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...

Q:

This assignment is about the following algorithm, which multiplies two square matrices A and B to produce a new square matrix C. Each matrix has size n n. 1 for i := 1 to n 2 for j := 1 to n 3 c ij...

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

You are given a square matrix of size N x N ( where 1

Q:

5. (1 point) K=_ Evaluate the following determinant. 9. (1 point) A square matrix A is skew-symmetric if A = -A. If A is an a X a skew-symmetric matrix where n is odd, prove that dot(A) = 0. Proof:...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

In order to use the routines PLUFactorization and SolvingPhase, you will need to dynamically allocate the matrix A and the vectors b, x, and ipivot. The beginning of your main program should be:...

Q:

Kai, a long-term Australian resident, decided to move overseas permanently, leaving during June 2016. Accordingly he entered into the following transactions: a, He sold his Mitsubishi station wagon...

Q:

Go to finance.yahoo.com and find the current stock prices for Southwest Airlines (LUV), Harley Davidson (HUG) and Starwood Resorts and Hotels (HOT). Get a quote for American Express (AXP) and follow...

Q:

r a firm with 7 0 % equity, and 3 0 % debt in their capital structure, which corporate action ould have the biggest reduction in WACC? a stock dividend a share buyback a bond issuance ( proceeds are...

Q:

1. How is the internal rate of return on a project computed? What does it measure?

Q:

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

Q:

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...

Q:

(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...

Q:

1) Davis Company produces three products: A, B, and C from the same process. Joint costs for this production run are $2,100. Pounds Sales price per lb. at split-off Disposal cost per lb. at split-off...

Q:

E19-25 (LO3) (NOL Carryback and Carryforward, Valuation Account Needed) Meyer reported the following pretax financial income (loss) for the years 2015-2019. 2015 $240,000 2016 350,000 2017 120,000...

Q:

Hardaway earned $121,000 of compensation this year. He also paid (or had paid for him) $3,850 of health insurance (not through an exchange). What is Hardaway's AGI in each of the following...