If A is diagonalizable, show that each of the following is also diagonalizable. (a) kA, k any
Question:
(a) kA, k any scalar.
(b) U-1AU for any invertible matrix U.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 53% (13 reviews)
a Since A is diagonalizable let P 1 AP D be diagonal Then P 1 kAP ...View the full answer
Answered By
Ayush Mishra
I am a certified online tutor, with more than 3 years of experience in online tutoring. My tutoring subjects include: Physics, Mathematics and Mechanical engineering. I have also been awarded as best tutor for year 2019 in my previous organisation. Being a Mechanical Engineer, I love to tell the application of the concepts of science and mathematics in the real world. This help students to develop interest and makes learning fun and easy. This in turn, automatically improves their grades in the subject. I teach students to get prepared for college entry level exam. I also use to teach undergraduate students and guide them through their career aim.
5.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Show that each of the following matrices is nonsingular but not diagonalizable. a. b. c. d. 003 3 6-43 332 120 012 0
-
Show that each of these is diagonalizable. (a) (b) x,y,z scalars 1 1
-
Show that each of the following transition matrices reaches a state of equilibrium? (a) (b) (c) (d) 0.4 0.2 0.6 0.8 5 100 0.3 0.1 0.4 0.2 0.4 0.0 0.5 0.5 0.6
-
A common stock pays an annual dividend that increases by 4% annually and sells for $35 per share. If the market rate of return on this stock is 8%. What is the amount of the ?last dividend paid $1.53...
-
What is meant by using bases for setting a preliminary judgment about materiality? How will those bases differ for the audit of a manufacturing company and a government unit such as a school district?
-
Answer all parts for the following DFA M and give reasons for your answers. a. Is M, 0100 A DFA ? b. Is M, 011 A DFA ? c. Is M A DFA ? d. Is M, 0100 A REX ? e. Is M EDFA? f. Is M,M EQDFA? 1 0,1
-
The calculation of solar radiation impinging on a surface is of importance in many applications, for example, design of solar collectors, temperature control of buildings, etc. Your goal is to review...
-
A review of emergency room records at rural Millard Fell more Memorial Hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a...
-
Units Beginning work in process inventory 32,000 Percent Complete 65% Percent Complete 35% Units started this period 410,000 Completed and transferred out 412,000 Ending work in process inventory...
-
Please solve this problem using C language Hacker Industries has a number of employees. The company assigns each employee a numeric evaluation score and stores these scores in a list. A manager is...
-
In each case find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P such that P-1AP is diagonal. (a) (b) (c) (d) 2 -4 365 121 110 011 (h) A=10 10 1 -1...
-
Give an example of two diagonalizable matrices A and B whose sum A + B is not diagonalizable.
-
When developing rates and premiums for a class of business, insurers need to take account of a range of internal factors, such as expenses and contingency loading. Outline how an underwriter must...
-
Rage For The Machine, Inc. budgeted $ 1 0 , 0 0 0 in overhead, actually incurred $ 1 1 , 0 0 0 in overhead, has a pre - determined overhead rate of $ 5 per direct labor hour, and used 2 , 5 0 0...
-
What role does technological innovation play in improving the standard of living, and how can governments and private enterprises incentivize and support innovation?
-
) Dividends Per Share Lightfoot Inc., a software development firm, has stock outstanding as follows: 25,000 shares of cumulative preferred 3% stock, $20 par, and 31,000 shares of $75 par common....
-
Discuss the impact of pharmacogenomics on personalized medicine and its implications for pharmacy practice.
-
Question 6 4 pts MEF Corporation had $600,000 in net income for the year ended December 31, 2018. What is Earnings per Share (in dollars and cents) if the company had 200,000 shares of common stock...
-
What is parametric polymorphism?
-
If the amplifier indicated by the box input impedance of oo, which of the following statements are true ? has an open loop gain as well as Feedback factor (\beta = 1/ R_1\) The feedback is voltage...
-
Show that ||A||F = ||AT||F.
-
Let A be a symmetric n n matrix. Show that ||A|| = ||A||1.
-
Let A be a 5 4 matrix with singular values 1 = 5, 2 = 3, and 3 = 4 = 1. Determine the values of ||A||2 and ||A||F.
-
What is Data Flow Diagram? Explain the Steps ti draw data flow diagram?
-
What is the purpose of data flow diagrams? Do data flow diagrams show system logic and decision points? Explain.
-
Online Shopping of clothes. Please solve the following part: Logical Model Design .. 1.0 Data Flow Diagram.. 1.1 Context Diagram.. 1.2 Level 0 Data Flow Diagram.. 1.3 Level 1 Data Flow Diagram.. 1.4...
Study smarter with the SolutionInn App