Show that if A is both diagonalizable and invertible, then so is A-1.

Question:

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 12:06 PM

See More Questions

Show that if A is nonsingular and diagonalizable, then A-1 is diagonalizable?
Show that if A is diagonalizable, with all eigenvalues less than 1 in magnitude, then Ak tends to the zero matrix as k .
(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...
1. Determine and confirm purchasing requirements for at least six (6) of the goods listed in the knowledge evidence. 2.Make purchase arrangements for the goods to meet different: End product...
Arthur Andersen Enterprise Group/National Small Business United, Washington, conducted a national survey of small-business owners to determine the challenges for growth for their businesses. The top...
Predict the hybridization, geometry, and bond angles for the carbon and nitrogen atoms in acetonitrile (CH3C N:).
What is the systems model of T&D? Discuss how HRIS T&D applications can assist in carrying out the steps in the systems model.
Assume you are given the following abbreviated financial statement. ($ in millions) $150.0 Fixed and other assets .............. 200.0 Total assets ................... $350.0 Current liabilities...
Transaction: The company paid $500 on January 1 for January's rent. In the table below, show the effect of the transaction above to each of the categories below (Assets, Liabilities, Equity) and the...
The statute is Georgia Code Ann. 11-2-314. The title of the statute is "Implied warranty: merchantability; usage of trade." The question is whether there is an implied warranty of merchantability....
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three-dimensional. Is it possible that A is not diagonalizable? Justify your answer.
Show that if A has n linearly independent eigenvectors, then so does AT.
a. Stomach cancer and consumption of barbecued foods, which are known to contain carcinogenic (cancercausing) substances. b. Self reported level of stress and blood pressure.
Assess the cost-effectiveness of a roof retrofit using a SIS for a Golden, CO, house that has an overall BLC of 400 W/C and roof insulated with RSI-5.9 with an exposed area of 180 m 2 . Estimate the...
Explain why groups play a vital role in our personal and professional lives.
Determine the annual electricity savings when the condensing temperature is reduced on average by 5C by an automatic controller for a 500-ton reciprocating chiller with a seasonal COP of 3.8. Assume...
For the same retrofit defined in Problem 11.7, (i) evaluate the cost-effectiveness of LED-integrated controls for various lifetimes ranging from 5 years to 30 years (use a 5-year increments), (ii)...
How would the wage rate and employment for the Escondida miners be determined in a competitive market? Workers at BHP Billitons Escondida mine in Chile, the worlds largest copper mine, have been...
In all problems, calculate dollar amounts accurate to the cent, and percent amounts accurate to the nearest 0.01%. Calculate the missing value for Problems. Initial value Final value Percent change ?...
The cash records of Holly Company show the following four situations. 1. The June 30 bank reconciliation indicated that deposits in transit total $720. During July, the general ledger account Cash...
Determine which sets are bases for R 3 . Of the sets that are not bases, determine which ones are linearly independent and which ones span R 3 . Justify your answers. 1 -4 [F] 2 -5 -3 6
Find bases for the null spaces of the matrices given. Refer to the remarks that follow Example 3. Data from in Example 3 0-3 0 1 -5 3-2 2 4 1-2
Find an explicit description of Nul A by listing vectors that span the null space. 1 -2 A = 0 0 0 0 4 0 0 1-9 0001
ABC Inc. curently has a share price of $44. If they are paying a dividend of $1.13, with a cum dividend date of November 1, would would you expect their share price to be on November 2nd? Please give...
Does China benefit from a weak currency?Does Us benefit from a strong currency? Why? Please explain
You purchased 10 ASD June 45 puts and the company declares a 10% stock dividend. How are the terms of the option contract then changed?

Show that if A is both diagonalizable and invertible, then so is A-1.

Question:

Step by Step Answer:

If A is diagonalizable then A PDP 1 for some invertible P and diag...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions