Question: Let A be diagonalizable with real eigenvalues and assume that Am = I for some m 1. Show that A2 = I.

Let A be diagonalizable with real eigenvalues and assume that Am = I for some m ≥ 1.
Show that A2 = I.

Step by Step Solution

★★★★★

3.41 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let A be diagonalizable with A m I If is any eigenval... 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

950-M-L-A-L-S (6341).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Consider the matrices Note that the two matrices are the same except for their (2, 2) entries. (a) Use MATLAB to compute the eigenvalues of A and B. Do they have the same type of eigenvalues? The...

Q:

Let A be an n n matrix with distinct real eigenvalues 1,2 . . . . n. Let be a scalar that is not an eigenvalue of A and let B = (A - I)-1. Show that (a) The scalars j = l/(j - ), j = 1,... ,n are...

Q:

Let a and b be real numbers. Find the eigenvalues and corresponding eigenspaces of over the complex numbers. a b

Q:

1. Find the eigenvalues and corresponding eigenspaces for each of the following matrices: 2. Let A be an n x n matrix (a) Prove that A is singular if and only if A = 0 is an eigenvalue of A. (b) Lal...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

12. Find the characteristic polynomial and the real eigenvalues of (3 13. Find the characteristic polynomial and the real eigenvalues of (2 1). 14. Find the characteristic polynomial, the real...

Q:

,, kindly solve Consider the Linear Regression Model 1. For any X = x, let Y = x8 + U, where B E R*. 2. X is exogenous. 3. The probability model is { f (u; ) is a distribution on R : E, [U] = 0, Var,...

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:

Could you please help with question 326? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real numbers in...

Q:

Could you please help with question 324 and 325? Thanks Exercise 309 Exercise 310 Theorem 3 Exercise 311 Exercise 312 75 5.8 Real symmetric matrices Real symmetric matrices play the role of real...

Q:

The human resources department at Harold Logistics is responsible for selecting and appointing employees, approving pay rates and promotions, and processing employee terminations. The payroll...

Q:

A company estimates an allowance for inventory obsolescence. However, this estimate is sensitive to changes in the short term. What are the disclosures required by current GAAP?

Q:

13 Here are two calculation cards. A 6+96-9) B (+) (+) Read what Sofia says. Is Sofia correct? Show all your working. The answer to card B divided by the answer to card A is 96.

Q:

What are the major differences and similarities among project portfolio management, program management, and managing multiple projects?

Q:

Given (a) Compute the singular value decomposition of D (b) Find the value of ||D||2. 0004 0020 3000

Q:

Show that if D is an n à n diagonal matrix, then ll D112 = max (ldil)

Q:

D is an n n diagonal matrix, how do the value, ||D||1, ||D||2, and ||D|| compare ? Explain your answer.

Q:

Question 50 1 Imagine a sample with n = 49 and a mean of 95 that comes from a population with a standard deviation of 14. Based on these data, what would be the 80% confidence interval for the...

Q:

The Landers Corporation needs to raise $1.70 million of debt on a 20-year issue. If it places the bonds privately, the interest rate will be 12 percent. 25000 dollars in out-of-pocket costs will be...

Q:

a comparable - risk bond is 6 percent. a . Compute the bond's yield to maturity. b . Determine the value of the bond to you given the market's required yield to maturity on a comparable - risk bond....