Question: Prove that if A is a diagonalizable matrix with only one eigenvalue , then a is of the form A = l. (Such a matrix

Prove that if A is a diagonalizable matrix with only one eigenvalue λ, then a is of the form A = λl. (Such a matrix is called a scalar matrix).

Step by Step Solution

★★★★★

3.45 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Suppose that A is diagonalizable and that is i... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

859-L-A-L-S (2566).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that if A is a diagonalizable matrix such that every eigenvalue of A is either 0 or 1, then A idempotent (that is, A2 = A).

Q:

(a) Show that if D is a diagonal matrix with nonnegative entries on the main diagonal, then there is a matrix S such that S2 = D. (b) Show that if A is a diagonalizable matrix with nonnegative...

Q:

If A is a diagonalizable matrix and all of its eigenvalues satisfy ||

Q:

A scalar matrix is a square matrix of the form I (I the identity matrix), for some scalar ; i.e. a scalar matrix is a diagonal matrix in which all diagonal entries are equal a) Prove that if a square...

Q:

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Q:

(a) Show that the only diagonalizable matrix A that has only one eigenvalue λ is the scalar matrix A = λI. (b) Is diagonalizable? 2

Q:

3. (10 points) If possible, give an example of the following. If it is not possible, write "not possible". (a) A 5 x 3 matrix, X, in RREF, such that dim(Col(X")) = 2, and dim(Null(X)) = 3. (b) A 3 x...

Q:

HEY CAN YOU HELP ME SOLVE THE FOLLOWING QUESTIONS: 63, 65, 73, 81, 82, 83 5.3 Diagonalization of Matrices 323 57. [_7 3]: ([:] . ): 43 74. Find a 2 x 2 matrix having eigenvalues 7 and -4, with 58. 2...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

I am stuck on this problem. I need to know how to solve it and part of that is knowing what I have done wrong in my current attempts to solve it. I have attached my work, which is incomplete, and a...

Q:

Refer to the information in QS 6-5 and assume the perpetual inventory system is used. Determine the costs assigned to ending inventory when costs are assigned based on weighted average. December 7 10...

Q:

Course: Civil-Military Relations Work: The Soldier and the State: The Theory and Politics of Civil-Military Relations (1957). author:Samuel P. Huntington All I need is to summarize this work briefly...

Q:

Take an edition of a leisure or tourism journal, such as Leisure Studies or Annals of Tourism Research, and ascertain, for each article: why the research was conducted; how it was funded; and who or...

Q:

Use predictive mean matching to multiply impute cost 10 times per missing observation. Describe graphically the distributions of imputed values and briefly compare these to distributions of...

Q:

Refer to check digit codes in which the check vector is the vector c = [1, 1, . . . , 1] of the appropriate length. In each case, find the check digit d that would be appended to the vector u. u =...

Q:

Refer to check digit codes in which the check vector is the vector c = [1, 1, . . . , 1] of the appropriate length. In each case, find the check digit d that would be appended to the vector u. u [1,...

Q:

Refer to check digit codes in which the check vector is the vector c = [1, 1, . . . , 1] of the appropriate length. In each case, find the check digit d that would be appended to the vector u. u =...

Q:

A portfolio is any collection of financial assets and investments. Let's say that out of $100,000 you invest $50,000 in Stock A and $50,000 in Stock B. This is a two-stock portfolio. You can change...

Q:

(b) John is going to retire in 10 years. He is planning to build a retirement fund that he would like to receive at the end of 10 years from now. Company X offers a package of two investment...

Q:

3. Suppose that CME September 2024 Canadian dollar futures contract has a price of $0.7950 per CAD. You believe the spot price in September 2024 will be $0.7900 per CAD. Assume that you take a short...