Question: Show that (A B)T = ATBT if and only if A and B are square commuting matrices.

Show that (A B)T = ATBT if and only if A and B are square commuting matrices.

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If A has size m n and B has size n p then AB T has size p m Further AT has ... 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

Document Format (1 attachment)

Word file Icon

952-M-L-A-E (1719).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Show that (a) (b) Res zt) -2 cos (TI). exp(zt) Res sinhz

Q:

Show that (a) (b) (c) 1.

Q:

Show that (a) (b) (c) Res z=-12+1 v2 Log z +2i Res i (22+1) 212 1 -i Res17 i + 82

Q:

Problem 1.4 (a) Let A, B = B* " he two stochastic matrices. Show that A - B is a stochastic matrix. ib) Let A, B = R he two stochastic matrices. Let A= (0,1). Show that A- 4 + (1 - A)- B 15 a...

Q:

please help me solve problem 1 and problem 2 6 wt ' \\" \" {r . i , ezzaEETFme MATH 217 - LINEAR ALGEBRA HOMEWORK 3, DUE Thursday, September 23, 2021, at 11:59pm 2 5 Problem 1. Determine whether the...

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:

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:

Please explain how to solve step by step and name any rules or theorems used. The following is from Chiang's fundamental mathematical economics. 1. Given A = [_; ; ]. 8 - [8 -8]. andc =[! " ;]. find...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

Two n n matrices A, B are said to be simultaneously diagonalizable if there is a nonsingular matrix S such that both S-1 A S and S-1 B S are diagonal matrices. (a) Show that simultaneously...

Q:

Evaluate each of the following and express with an appropriate prefix: (a) (430 kg) 2, (b) (0.002 mg) 2, and (c) (230 m) 3.

Q:

There is a code of ethics when it comes to sociological. given this code of ethics. which of the founding fathers within sociological, was best suited for today's society? Founding Father (Auguste...

Q:

Condensed financial data of Blossom Company for 2 0 2 5 and 2 0 2 4 are presented below. Blossom Company Income Statement For the Year Ended December 3 1 , 2 0 2 5 Other revenues and gains Additional...

Q:

Write down the equations that describe the following models: a. GARCH(1,2) model b. AR(2)-ARCH(5) c. AR(3)-GARCH(2,1)

Q:

The figure shows vectors u, v, and w, along with the images T(u) and T(v) under the action of a linear transformation T :. Copy this figure carefully, and draw the image T(w) as accurately as...

Q:

In Exercises 1 and 2, mark each statement True or False. Justify each answer. 1. a. A linear transformation is a special type of function. d. Every linear transformation is a matrix transformation....

Q:

a. Show that ( is a linear transformation when b = 0. b. Find a property of a linear transformation that is violated when b ( 0. c. Why is ( called a linear function? RR

Q:

For the just completed year, Hanna Company had net income of $35,000. Balances in the companys current asset and current liability accounts at the beginning and end of the year were as follows:...

Q:

What is a fair price of a 2 5 - year semi - annual coupon bond, with a coupon rate of 6 . 8 4 % , a face value of $ 1 0 0 0 , and a yield - to - maturity of 7 . 0 5 % ? ( Answer to nearest $ 0 . 0 1 )

Q:

#1 You need to estimate the equity cost of capital for XYZ Corp. You have the following data available regarding past returns: a. What was XYZ 's average historical return? b. Compute the market's...