Show that if det(A) = I then adj (adj A) = A

Question:

Show that if det(A) = I then
adj (adj A) = A

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:48 AM

See More Questions

The Polar Decomposition: Prove that every invertible matrix A has a polar decomposition, written A = QB, into the product of an orthogonal matrix Q and a positive definite matrix B > 0. Show that if...
Let A be a nonsingular square matrix. (a) Prove that the product of the singular values of A equals the absolute value of its determinant: 1 2 ... n = |det A|. (b) Does their sum equal the absolute...
(a) Prove that if det A > 1, then A has at least one eigenvalue with || > 1. (b) If |det A| < 1, are all eigenvalues || < 1? Prove or find a counter example.
Certain environmental laws prohibit EPA from considering the costs of meeting various standards when the levels of the standards are set. Is this a good example of putting first things first or...
If you are a banker and expect interest rates to rise in the future, would you want to make short-term or long-term loans?
An industry analyst constructed a model describing the cost of building cars at plants operated by different manufacturers in North America. As a first step, the analyst regressed total production...
The following are the number of pounds per day shipped by a trucking company. It is suggested that the shipments be treated as a process. Because these data are not symmetrically distributed, you...
Transit Airlines provides regional jet service in the Mid-South. The following is information on liabilities of Transit at December 31, 2011. Transit's fiscal year ends on December 31. Its annual...
Discuss the role of real-time communication protocols in RTOS-based systems. How do these protocols ensure real-time data exchange while maintaining system stability and predictability ?
The following selected data are for Perron Importers Limited for its first three years of operations: Instructions Determine the missing amounts. TAKING IT FURTHER What information does the owner of...
Show that if A is singular then adj A is also singular.
Suppose that Q is a matrix with the property Q-1 = QT. Show that qij = Qij / det(Q)
Examine various household products and describe how they are joined and assembled. Explain why those particular processes are used for these particular applications?
Dove - Take care. Be safe. It all started with a beauty soap bar that grew into a global brand with an extensive product range. The beauty bar Dove was launched in 1957. With its 3/4 moisturising...
Anderson Corp. has the following information: Beginning Ending Inventory Inventory (1/1) (12/31) Direct Materials Inventory $20,000 $30,000 Work in Process Inventory $16,000 $18,000 Finished Goods...
B 15 16 1) Useful life of the equipment (years) 17 2) New equipment cost* 18 3) Equipment ship & install costs* C 19 4) Related equipment start-up costs* 20 5) Inventory increase. 21 6) Accounts...
Using the Information below of Opportunities and threats. , develop an EFE matrix using five (5) opportunities and five (5) threats. Discuss how you developed the EFE matrix and the outcome....
Your audit firm was appointed as auditors of Molteno (Pty) Ltd (following the resignation of the previous auditor) in the current year. Permission was obtained to consult the previous auditors. The...
For the following exercises, find all solutions exactly that exist on the interval [0,2). 1 2tan() = tan 2 ()
Several months have passed and the Managing Partner approved and properly filed the Complaint and properly submitted the Request for Production of Documents that you drafted. In fact, it has been 75...
Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample. (a) A square matrix with linearly independent column vectors...
If A1, A2, , Ak, is an infinite sequence of n Ã n matrices, then the sequence is said to converge to the n Ã n matrix , A if the entries in the ith row and jth column of the sequence...
Show that the Jordan block matrix Jn has = 1 as its only eigenvalue and that the corresponding eigenspace is span {e1}.
How crucial is it to understand the many sorts of speech contexts on a daily basis? Give one specific example. Here are the types of speech context: 1. Public Communication 2. Small Group...
Enmebaragesi of Kish, Inc. has sales of $282,000, cost of goods sold of $206,000, depreciation of $4,200, and interest expense of $22,000. The tax rate is 30.8 percent. What is the times interest...
Inkishush and Company has a book value per share of $10.35, earnings per share of $2.23, and a price-earnings ratio of 19.4. What is the market-to-book ratio?

Show that if det(A) = I then adj (adj A) = A

Question:

Step by Step Answer:

If det A 1 then adjA det AA ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions