Let A be an idempotent matrix. (a) Show that An = A for all integers n

Question:

Let A be an idempotent matrix.
(a) Show that An = A for all integers n ≥ 1.
(b) Show that In - A is also idempotent.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 06:58 AM

See More Questions

Let A be an idempotent matrix (that is, A2 = A). Show that = O and = 1 are the only possible eigenvalues of A.
A matrix A is idempotent if A2 = A. Show that the only possible eigenvalues of an idempotent matrix are = 0 and = 1. Then give an example of a matrix that is idempotent and has both of these two...
An n Ã n matrix P is called an idempotent if P2 = P. Show that: (a) I is the only invertible idempotent. (b) P is an idempotent if and only if I - 2P is self-inverse. (c) U is self-inverse if...
Calculate the investment return, BAR, and ALPHA of the following investment, all over one year. Market return .12 or 12% investment in Tesla stock, $15000 , then sold at end of year for $32000, bet...
Harris Segal, marketing director for North-Central Power and Light, is about to begin an advertising campaign promoting energy conservation. In trying to budget between television and newspaper...
Formic acid, HCHO 2 , is used to make methyl formate (a fumigant for dried fruit) and ethyl formate (an artificial rum flavor). What is the pH of a 0.12 M solution of formic acid? What is the degree...
Suppose you make 15 equal annual deposits of $$1,000$ each into a bank account paying 5% interest per year. The first deposit will be made one year from today. How much money can be withdrawn from...
Planning Procurement. An automobile manufacturer wants to award contracts for the supply of five different engine components. Some of the components are used in most models, while other components...
The output of the code below is #include #include int main(){ float x; x = floor(7.5); printf("%.2f ",x); return 0;}
Abhinav is a trader. Using the following information taken from Abhinavs books on 30 June 208: a. Prepare a trial balance at 30 June 208 b. Prepare an income statement for the year ended 30 June 208...
Let A and B be n n idempotent matrices. (See Exercise 19.) (a) Show that AB is idempotent if AB = BA. (b) Show that if A is idempotent, then AT is idempotent. (c) Is A + B idempotent? Justify your...
If A is an n x n matrix, then A is called nilpotent if Ak = O for some positive integer k. (a) Prove that every nilpotent matrix is singular. (b) Verify that is nilpotent. (c) If A is nilpotent,...
Which of the following equations might have the graph shown? (a) (x - 2) 2 + = 3 (b) (x + 2) 2 + y 2 = 3 (c) x 2 + (y - 2) 2 = 3 (d) (x + 2) 2 + y 2 = 4 (e) x 2 + y 2 + 10x + 16 = 0 f) x 2 + y 2 +...
A) Why loan sale by a bank is called an off-balance sheet activity? Explain B) How do financial intermediaries use economies of scale to lower their transaction cost?
Your old car has a value of of $1,800. You want to buy a new car with a sticker price of $19,750. The dealer says she will take your old car in trade and give you a loan of $17,900. How much are you...
In March, Adrian Saylor sold government bonds owned exclusively by him and with $ 6 , 4 5 0 of the proceeds opened a savings account in a bank in the name of " Mr . or Mrs . Adrian M . Saylor." In...
Please explain the behaviour why an investor purchases an insurance policy to lower risk exposure, while trading derivatives at the same time. Is it rational? (8 marks)
Assume the following information: Mexican one-year interest rate = 9% U.S. one-year interest rate = 3% Peso spot rate = 0.12 $/p Peso forward rate = 0.06 $/p If interest rate parity exists, how much...
The first production department of Stone Inc. reports the following for April. Compute the number of equivalent units of production for both direct materials and conversion for April using the...
Wimot Trucking Corporation uses the units-of-production depreciation method because units-of-production best measures wear and tear on the trucks. Consider these facts about one Mack truck in the...
Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) If Ax = b is any consistent linar system of m equations in...
Use Theorem 5.2.1 to determine which of the following are subspaces of P3. (a) All polynomials a0 + a1x + a2x2 + a3x3 for which a0 = 0 (b) All polynomials a0 + a1x + a2x2 + a3x3 for which a0, a1, a2...
Use Theorem 5.2.1 to determine which of the following are subspaces of Mnn. (a) All n x n matrices A such that AT = -A (b) All n x n matrices A such that the linear system Ax = 0 has only the trivial...
Identify an area of Financial Services where you feel significant opportunities lie in relation to process management. Why do you feel this?
1. Given the functions f(x) = x + 1 and g(x) = 3-x, determine an equation for the combined function y = f(x)+ g(x). 2. If f= {(-7, 1), (-5, 8), (3, 11), (5,-1)) and g = {(-6, 4), (-5, 3), (-1, 7),...
What is urban economics and what components of a city usually results in higher demand of a city's real estate. Describe at least three

Let A be an idempotent matrix. (a) Show that An = A for all integers n

Question:

Step by Step Answer:

a We prove this statement using induction The result is ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions