Concern the polynomial and an n n matrix C p called the companion matrix of p:
Question:
Concern the polynomialand an n × n matrix Cp called the companion matrix of p:
Let p(t) = a0 + a1t + a2t2 + t3, and let be a zero of p.
a. Write the companion matrix for p.
b. Explain why λ3 = a0 - a1λ - a2λ2, and show that (1, λ, λ2) is an eigenvector of the companion matrix for p.
Transcribed Image Text:
p(t)= ao + a₁t +...+ an-1t"-1 +t"
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 33% (3 reviews)
a b 0 ...View the full answer
Answered By
Joseph Njoroge
I am a professional tutor with more than six years of experience. I have helped thousands of students to achieve their academic goals. My primary objectives as a tutor is to ensure that students do not have problems while tackling their academic problems.
4.90+
10+ Reviews
27+ Question Solved
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
Question Posted:
Students also viewed these Mathematics questions
-
Let p(f) = a0 + a1f + a2t2 + t3, and let A be a zero of p. a. Write the companion matrix for p. b. Explain why 3 = - a0 - a1 - a22, and show that (1, , 2) is an eigenvector of the companion matrix...
-
Let A be a 4 Ã 3 matrix with a2 = a3. If b = a1 + a2 + a3, then the system Ax = b will have infinitely many solutions. In this case answer true if the statement is always true and false...
-
Let p() = (-1 )n(n - n-1n-1 -....- 1 - o) he a polynomial of degree n I (a) Show that if i, is a root of p() = 0 then i is an elgenvalue of C with eigenvector x = (in-1,, in-2...... i,1)T , (b) Use...
-
Alderon Industries manufactures chemicals for various purposes. One process that Alderon uses produces SPL-3, a chemical used in swimming pools; PST-4, a chemical used in pesticides; and RJ-5, a...
-
The following information was obtained from Acamac Corp.'s (Acamac) 2018 financial statements: Sales (all sales are on credit).........................$4,150,000 Accounts receivable on March 31,...
-
It is often said that one of the benefits of a diverse workforce is that employees will better understand and relate to their diverse customers. Does this justify making hiring decisions on protected...
-
How the California court system is structured
-
Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, uses 6 yards of material, and provides a profit...
-
1. Consider the Black-Scholes market. (a) Write out the dynamics of the assets in this market in the objective space. (b) Write out the dynamics of the assets in the risk neutral space. (c) Using the...
-
You saw an advertisement on the website of ABC Bank about a new product called "Best Protection Deposits". The information about the product is listed below: Deposits Required Guaranteed Interest...
-
With A and D as in Example 2, find an invertible P 2 unequal to the P in Example 2, such that A = P 2 DP 2 -1 . Data from in Example 2 7 -[41] EXAMPLE 2 Let A = where P Find a formula for Ak, given...
-
Concern the polynomial and an n n matrix C p called the companion matrix of p: Let p(t) = 2t - 3t 2 + t 3 . Write the companion matrix for p(t) and use techniques to find its characteristic...
-
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In + Xx X
-
The U.S.S. Enterprise (NCC-1701) approaches an unknown system with a Black Hole at the center. One of the planets in this system is observed to have an orbit with a radius of R = 3.3 AU and a period...
-
Kevin Smith is a senior sales manager at Tradeco Ltd. He worked for the same company for a number of years and was using his good friend's neighbor to do his taxes but this year he got a reassessment...
-
DETERMINING NET CASH FLOW FROM INVESTING ACTIVITIES The ABC Corporation reported the following information: January 1 December 31 Equipment $68,000 $114,500 Accumulated depreciation 19,500 21,800...
-
Bob Andy Music Mart received his bank statement for the month of December which showed an overdraft balance of 113,209. Being anxious of his cash situation he conducted an audit of his cash book...
-
why does it matter if photographs lie? Use examples of your own research?
-
A mining company estimates that the marginal cost of extracting tons of copper ore from a mine is 0.6 + 0.008x, measured in thousands of dollars per ton. Start-up costs are $100,000. What is the cost...
-
Proposals have been made to ?sail? spacecraft to the outer solar system using the pressure of sunlight, or even to propel interstellar spacecraft with high-powered, Earth-based lasers. Sailing...
-
The following data show U.S. retail sales of canoes from 1980 through 1997, with data in thousands of boats. a. Construct a graph of the time series. Does the overall trend appear to be upward or...
-
The following data describe quarterly residential natural gas sales from 1991 through 1994. Determine the quarterly seasonal indexes, then use these indexes to deseasonalize the original data....
-
The National Association of Railroad Passengers has reported the following data describing U.S. commuter train ridership. Year 1995 1996 1997 1998 1999 2000 Riders 42.2 45.9 48.5 54.0 58.3 61.6...
-
2. What is the potential asymmetry in the effect of interest rates on Investment? 3. Describe whether the following changes cause AD to shift to the right, to the left or to not shift all. (Draw a...
-
1.For an open economy with high capital mobility and fixed exchange rates, explain why an expansionary fiscal policy would be more successful in stimulating the economy, and why an expansionary...
-
Complete the following graphing assignment. You are given the following information about the Goodell Cargo Shipping Company, Inc. in Rochester, Minnesota. From 2009-2022, the prices of their cargo...
Study smarter with the SolutionInn App