Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I

Question:

Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I - A.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:05 AM

See More Questions

(a) Show that if A is a square matrix with linearly independent columns, then A+ = A-1. (b) If A is an m n matrix with orthonormal columns, what is A+?
(a) Prove that if A is a square matrix, then A and AT have the same eigenvalues (b) Show that A and AT need not have the same eigenspaces.
(a) Show that if D is a diagonal matrix with nonnegative entries on the main diagonal, then there is a matrix S such that S2 = D. (b) Show that if A is a diagonalizable matrix with nonnegative...
In Exercises 1126, determine whether each equation defines y as a function of x. x + y = 16
What is meant by the expressions order winners and order qualifiers? What was the order winner(s) for your last purchase of a product or service?
In practice, bonds issued in the United States usually make coupon payments twice a year. So, if an ordinary bond has a coupon rate of 14 percent, the owner will receive a total of $140 per year, but...
The Caplow Company is a multi-divisional company. Its managers have been delegated full profit responsibility and complete autonomy to accept or reject transfers from other divisions. Division A...
A project will cost $50,000. The benefits at the end of the first year are estimated to be $10,000, increasing at a 10% uniform rate in subsequent years. Using an 8-year analysis period and a 10%...
Explain how the family empowered the business success story for Samsung. 200-300 words.
The income statement of Fezzik's Shoe Repair is as follows: On April 1, the Owner's Capital account had a balance of $12,900. During April, Fezzik withdrew $3,000 cash for personal use. Prepare...
A square matrix A is called idempotent if A2 = A. (The word idempotent comes from the Latin idem, meaning "same;' and potere, meaning "to have power:' thus, something that is idempotent has the "same...
Prove that if a symmetric matrix is invertible, then its inverse is symmetric also.
Which of the following is a false statement regarding enzymes? A. Enzymes are proteins that speed up metabolic reactions; B. Enzymes have specific substrates; C. Enzymes supply ATP to their...
Financial strength can be defined as the capacity to produce enough cash flows and earnings to pay creditors, investors, and other debts, as well as to cover expenses. Even though sales by themselves...
The RMS Titanic was the most technologically advanced liner in the world in the year 1912. At 11:40pm or Sunday, April 14 of that year, the Titanic struck an iceberg and sank in less than three...
1. A management consultant is hired by a manufacturing firm to determine the best site for its next production facility. The consultant has had several meetings with the company's senior executives...
The figure below shows that a pump is used to transfer water from a reservoir at ground level to a storage take that is elevated. The pump is located 10 ft above the water surface of the reservoir...
P6-3 (Algo) Comparing and Contrasting the Effects of Inventory Costing Methods on Financial Statement Elements LO6-2, 6-3 Neverstop Corporation sells item A as part of its product line. Information...
A town council considers the question of closing down an adult theatre. The five men on the council all vote against this and the three women vote in favor. What is the probability we would get this...
Portal Manufacturing has total fixed costs of $520,000. A unit of product sells for $15 and variable costs per unit are $11. a). Prepare a contribution margin income statement showing predicted net...
Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x = x +...
Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x = 2x -...
Find the general solution to the given system of differential equations. Then find the specific solution that satisfies the initial conditions. (Consider all functions to be functions of t.) x 1 = x...
Practice Problem 1 The stockholders equity accounts of Bramble Corp. on January 1, 2017, were as follows. Preferred Stock (6%, $100 par noncumulative, 4,400 shares authorized) $264,000 Common Stock...
JVCU Which of the following is considered cash for financial reporting purposes? 1 JVCU Which of the following is considered cash for financial reporting purposes? 1
Required information The Foundational 15 [LO8-2, LO8-3, LO8-4, LO8-5, LO8-7, LO8-9, L08-10) (The following information applies to the questions displayed below.) Morganton Company makes one product...

Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I

Question:

Step by Step Answer:

To show that A 1 2I A it suffices to sho...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions