Let A be an n n matrix. Prove that the characteristic polynomial of A has degree
Question:
Prove that the characteristic polynomial of A has degree n.
Prove that the coefficient of λn in the characteristic polynomial is 1.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (6 reviews)
Let a ij denote the ijth entry of A Then the charact...View the full answer
Answered By
Salmon ouma
I am a graduate of Maseno University, I graduated with a second class honors upper division in Business administration. I have assisted many students with their academic work during my years of tutoring. That has helped me build my experience as an academic writer. I am happy to tell you that many students have benefited from my work as a writer since my work is perfect, precise, and always submitted in due time. I am able to work under very minimal or no supervision at all and be able to beat deadlines.
I have high knowledge of essay writing skills. I am also well conversant with formatting styles such as Harvard, APA, MLA, and Chicago. All that combined with my knowledge in methods of data analysis such as regression analysis, hypothesis analysis, inductive approach, and deductive approach have enabled me to assist several college and university students across the world with their academic work such as essays, thesis writing, term paper, research project, and dissertation. I have managed to help students get their work done in good time due to my dedication to writing.
5.00+
4+ Reviews
16+ Question Solved
Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
Question Posted:
Students also viewed these Linear Algebra questions
-
Let A be any n ( n real matrix. (a) Prove that the coefficient of (n-1 in the characteristic polynomial of A is given by - Tr(A). (b) Prove that Tr(A) is the sum of the eigenvalues of A. (c) Prove...
-
The Cayley-Hamilton Theorem: Let pA () = det(A - I) be the characteristic polynomial of A. (a) Prove that if D is a diagonal matrix, then pD(D) = O. (b) Prove that if A is complete, then pA(A) = O....
-
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...
-
Rio Tinto is a listed company in the mining and metals production industry. Some information drawn from its 2020 annual report is shown below. Safety and health performance 2020 2019 2018 Fatalities...
-
The fifth Case Study (pages 538544) discussed the big global imbalances of the 2000s and suggested that one can analyze factors determining world real interest rates in terms of the balance between...
-
LAG Network Inc.?s balance sheet and income statement are as follows: Additional information regarding LAG Network Inc.?s activities during 2020: a. Equipment is purchased for $14,400 cash. b. 8,200...
-
For each of the following sets of data, (1) calculate the mean of the scores \(\left(\mathrm{X}^{-} ight),(2)\) calculate the deviation of each score from the mean \(\mathrm{X}-\mathrm{X}^{-}\), and...
-
The wearever Shoe Company is going to open a new branch at a mall, and company manager are attempting to determine how many sales-people to hire Based on an analysis of mall traffic. The company...
-
at the beginning of the year addisons companys assests are 1 5 8 0 0 0 and its equity is 1 1 8 5 0 0 . during the year assets increase 8 0 0 0 0 and liabilities increase 4 8 0 0 0 . what is the...
-
What is the maximum number of super keys for the relation R1(P, Q, R, S) with R as the key? () 6 (b) 8 () 16 (d) 32
-
Let A be a 2 Ã 2 matrix, and call a line through the origin of R2 invariant under A if Ax lies on the line when x does. Find equations for all lines in R2, if any, that are invariant under the...
-
Use the result in Exercise 16 to show that if then the solutions of the characteristic equation of A are Use this result to show that A has (a) Two distinct real eigenvalues if (a - d)2 + 4bc > 0 (b)...
-
Graph the inequality. 2x + y 6
-
Teresa is a 32-year-old woman in your practice who frequently misses her appointments and at other times shows up without an appointment, often in crisis. She currently uses alcohol and tobacco, and...
-
Weaver Corporation had the following stock issued and outstanding at January 1, Year 1: 1. 73,000 shares of $4 par common stock. 2. 7,000 shares of $90 par, 6 percent, noncumulative preferred stock....
-
1. Review the following tracings, identify the type of BBB, and then explain how you determined your answers 2. Review the following tracing. Do you suspect left ventricular hypertrophy? Explain how...
-
Sweeten Company had no jobs in progress at the beginning of the year and no beginning inventories. It started, completed, and sold only two jobs during the year-Job P and Job Q. The company uses a...
-
Required: Determine the missing amount for each separate situation involving work in process cost flows. (1) (2) (3) Total manufacturing costs $151,500 $218,500 Work in process inventory, beginning...
-
In Problem find the solution set. 3 - y 4(y - 3)
-
Differentiate. y = ln(3x + 1) ln(5x + 1)
-
How many solutions will the linear system Ax = b have if b is in the column space of A and the column vectors of A are linearly dependent? Explain.
-
Let A be an m n matrix with m > n. Let b Rm and suppose that N(A) = {0}. (a) What can you conclude about the column vectors of A? Are they linearly independent? Do they span Rm? Explain. (b) How...
-
Let A and B be row equivalent matrices. (a) Show that the dimension of the column space of A equals the dimension of the column space of B. (b) Are the column spaces of the two matrices necessarily...
-
Aspen Company's non-callable bonds currently sell for $905. They have a 15-year maturity, an annual coupon of $70, and a par value of $1,000. What is their yield to maturity? Your answer should be...
-
Vail Resorts, Inc., owns and operates 11 premier year-round ski resort properties (located in the Colorado Rocky Mountains, the Lake Tahoe area, the upper midwest, Vermont, and Australia). The...
-
Run Number m, (0.1g) m (0.1g) 1 250.1 320.7 After performing the experiment shown in Figure 5.2-1, a student obtained the following result: a meas (7) F(N) 1.140.0007 2 260.2 310.6 0.7760.0061 3...
Study smarter with the SolutionInn App