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 for p ...

a b Since Thus That is which ...

Let p(f) = a0 + a1f + a2t2 + t3, and let A be a zero of

Question:

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 λ3 = - a0 - a1λ - a2λ2, and show that (1, λ, λ2) is an eigenvector of the companion matrix for p.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra and Its Applications

ISBN: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:09 PM

See More Questions

If F is a field, let S F[x] where f(x) = anxn + an-1xn-l + + a2x2 + a1x + a0 S if and only if an + an-1 + + a2 + a1 + a0 = 0. Prove that S is an ideal of F[x].
(a) Let f(x) = anxn ++ a1x + a0 Z[x]. If r/s Q, with gcd(r, s) = land/(r/s) = 0, prove that s|an and r|a0. (b) Find the rational roots, if any exist, of the following polynomials over Q. Factor...
Let f be defined on [a, b], and let the nodes a = x0 < x1 < x2 = b be given. A quadratic spline interpolating function S consists of the quadratic polynomial S0(x) = a0 + b0(x x0) + c0(x x0)2 on...
The monochromatic emissivity of a diffuse-surface at 1600 K varies with wavelength in the following manner : = 0.4 for 0
A data set contains the following eight values. 4 3 0 5 2 9 4 5 a. Find the range. b. Find the mean absolute deviation. c. Find the sample variance. d. Find the sample standard deviation. e. Find the...
1. Rank the following compounds in order of increasing acidity. 2. Indicate which compounds would be more than 99% deprotonated by a solution of sodium ethoxide in ethanol. () (b) () (d) () (f)...
Consider the contamination discussion at the start of this section. The information is summarized here. Probability of Failure Level of Probability of Contamination Level 0.1 High 0.2 0.005 Not high...
What are the likely reasons and rationalizations Matt will give for making the payments discussed in the case?
We use checksum in both TCP and UDP to detect errors. Assume you have the following 2 bytes: 11011100 and 01100111. What would be the 1s complement of the addition of the above two bytes? Make sure...
The Balance Sheet of the General Fund of the City of Monroe as of December 31, 2019, follows. CITY OF MONROE General Fund Balance Sheet As of December 31, 2019 Assets Cash $ 503,000 Taxes receivable...
Use mathematical induction to prove that for n > 2, ..+ an-12"-1 +1") det(C, A1) = (-1)"(o + ajd + = (-1)" p(2)
Let p be the polynomial in exercise 22. And suppose the equation p(f) = 0 has distinct roots Î»1, Î»2, Î»3. Let V be the Vandermonde matrix (The transpose of V was...
Outline three different Grignard syntheses for 3-methyl-3-hexanol.
Big Ideas Ltd decided to buy parts of a competitor's business, which was cutting back operations. For a price of $4.2 million ($1 million down payment and the rest in four equal annual instalments,...
Revesby Ltd started business on 1 July 2016 and had the following transactions on 1 July: a. Issued 500 000 shares of $1 for $500 000 cash. b. Bought equipment for $400 000, paying cash. The...
The following data is extracted from the accounting records of ABC Limited at 30 June 2016. What is the balance of current liabilities at 30 June 2016? $ Equipment Accounts receivable 400 000 90000...
Quick Express, a leading courier company, sold a small delivery truck that had been used in the business for five years. The records of the company reflected the following: What is the journal entry...
Give examples of items that are revenue for a given period but not receipts for that period, items that are receipts but not revenue, and items that are both revenue and receipts.
Lavadora Company produces dishwashers for 108 retail outlets. Of the 108 retail outlets, 102 are small, separately owned appliance stores, and six are large retail chains. The six large retailers buy...
Consider the combustion of methanol below. If 64 grams of methanol reacts with 160 grams of oxygen, what is the CHANGE in volume at STP. 2CH3OH(g) + 3O2(g) 2CO2(g) + 4H2O(1) The volume decreases by...
A is an n n matrix. Justify each answer. (T/F) Finding an eigenvector of A may be difficult, but checking whether a given vector is in fact an eigenvector is easy.
A and B are n n matrices. Justify each answer. (T/F) If + 5 is a factor of the characteristic polynomial of A, then 5 is an eigenvalue of A.
Is a steady state vector for Justify your answer. q [3/7 4/7
1 Mandatory requirement: Students are required to complete Budget on the provided Excel 2 3 4 5 5 B spreadsheet template. (For the purpose of Budget calculation in the assessment, ignore all GST...
A company has Rs 4 per year carrying cost on each unit of inventory, an annual usage of 50,000 units and an ordering cost of Rs 100 per order. Calculate the economic order quantity. What shall be the...
The company decided to make some changes to its operations based on the actual results and the variance analysis. The plan is to maintain the selling price of the product at RM100 per unit and the...

Let p(f) = a0 + a1f + a2t2 + t3, and let A be a zero of

Question:

Step by Step Answer:

a b Since Thus That is which ...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions