Explain why each of the following algebraic rules will not work in general when the real numbers

Question:

Explain why each of the following algebraic rules will not work in general when the real numbers a and b are replaced by n × n matrices A and B.
(a) (a + b)2 = a2 + 2ab + b2
(b) (a + b)(a - b) = a2 - b2

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:43 AM

See More Questions

Explain why each of the following is or is not a valid probability distribution for a discrete random variable x: a. b. c. d. 32 23 3 2 p(x) 25 50.20 20 p(x) -3 1.03 3 15 20 40 5 p(x) 40.35
Explain why each of the following is used in experiments. You may refer to an example in the chapter if it makes it easier to explain. a. Placebo treatments b. Control groups
Explain why each of the following integrals is improper. a. b. c. d. cot x dx
Show that an emission tax and an absolute emission standard are equivalent instruments to regulate a polluting monopolist if and only if the standard is binding.
Chicago Avenue Bank has the following assets: What is Chicago Avenue Banks asset portfolioduration? Duration (in years) 0.55 2.35 5.90 Asset Value T-bills Consumer lons $40,000,000 Commercial Loans...
An officer for a large construction company is feeling nervous. The anxiety is caused by a new excavator just released onto the market. The new excavator makes the one purchased by the company a year...
Use the wine quality data in Table B. 11 to construct a regression model for quality using the stepwise regression approach. Compare this model to the one you found in Problem 10.4, part a. Data From...
Why has eBay succeeded as an online auction marketplace while so many others have failed?
Amy wants to take the next five years off work to travel around the world. She estimates her annual cash needs at $34,000 (if she needs more, she will work odd jobs). Amy believes she can invest her...
Papas Pizza Heaven serves take-out pizza from three locations in Columbus, Maryland. Papas considers each pizza delivered (even if the order is for two or more pizzas) as the cost object for the...
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, ...
Will the rules in Exercise 20 work if a is replaced by an n n matrix A and b is replaced by the n n identity matrix I?
Cinergy is a utility company that provides gas and electric service in Ohio, Kentucky, and Indiana. The companys dividend yield is 6.6 percent. Starbucks, a well-known retailer of coffee products,...
A mechanical wave travels the length of a 2 7 m long string stretched to a tension of 7 6 N in 0 . 2 4 s . Find the mass of the string ( in g ) .
Calculate the area of r = 7 . 3 plus or minus 0 . 2 cm , I calculated the area to be A = 1 6 7 . 4 1 5 but i am struggling with calculating the uncertainty.
A 3 . 5 - kg mass weighs 3 5 N and is held 6 . 8 m above the ground. Calculate its potential energy relative to the ground. Round to the whole Joule. A student lifts a 1 . 2 k g bag from her desk,...
A water wave is confined in a channel that is 1 5 m wide. These boundaries create standing waves with an anti - node at each side of the channel. What is the longest wavelength that will form between...
b. What is the mathematical relationship (not the equation) between the voltage, V, applied to a resistance, R, and the current, I, flowing through it? c. Write the equation that relates the...
Problem refer to the Venn diagram below for events A and B in an equally likely sample space S. Find each of the indicated probabilities. P((A B)) S A B 12 38 23 27
Use Stokes' Theorem to evaluate f(y+sin x) dx+(z+cos y) dy+rdz, where C is the rve r(t) = (sint, cost, sin 2t), t = [0, 2].
Let A be the matrix Find p(A). p(x) = 2x2 - x + 1 3
Which of the following are elementary matrices? (a) (b) (c) (d) 3 -5 1 100 100 2001 0010 0100 2000
(a) Find elementary matrices E1, E2 and E3 such that E3E2E1A = I3. (b) Write A as a product of elementary matrices Let 231 040 100
LaToya Limmons is the manager of the Human Resources (HR) department and Javier Jartin is the manager of the sales department for a production company headquartered in the United States but also has...
The beam AD is fixed to a rigid wall at A and is supported by props at B and C as shown in figure 1. In sections AB and BC, the flexural rigidity is EI, but in section CD the flexural rigidity is...
What is the meaning of 'framing' and how does it impact the way we negotiate? (Your own opinion)

Explain why each of the following algebraic rules will not work in general when the real numbers

Question:

Step by Step Answer:

a A B 2 A BA B A BA A BB A 2 BA AB B 2 In the case of real n...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions