Prove that if U is a nonsingular upper triangular matrix, then the diagonal entries of U-1 are

Question:

Prove that if U is a nonsingular upper triangular matrix, then the diagonal entries of U-1 are the reciprocals of the diagonal entries of U.

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:23 AM

See More Questions

(a) According to Exercise 5.2.12, the Grarn-Schmidt process can also be applied to produce orthonormal bases of complex vector spaces. In the case of Cn, explain how this is equivalent to the...
A square matrix is called upper triangular if all of the entries below the main diagonal are zero. Thus, the form of an upper triangular matrix is Where the entries marked * are arbitrary. A more...
Prove that if an upper triangular matrix is orthogonal, then it must be a diagonal matrix.
What are the advantages and disadvantages of decentralization? Would you prefer to work in a centralized or decentralized organization and why? What are opportunity costs and what are the economic...
As a consultant, you have been asked to recommend either a gainsharing plan or a profit-sharing plan for employees who work in the four regional distribution and warehousing facilities of a large...
A company uses an overhead absorption rate of $3.50 per machine hour, based on 32,000 budgeted machine hours for the period. During the same period the actual total overhead expenditure amounted to...
Consider the gasoline mileage performance data in Table B.3. a. Use the all-possible-regressions approach to find an appropriate regression model. b. Use stepwise regression to specify a subset...
On January 1, 2016, Palo Company acquires 80% of the outstanding common stock of Sheila Company for $700,000. On January 1, 2018, Sheila Company sells 25,000 shares of common stock to the public at...
1.1 A network protocol can be defined as an established set of rules that determine how data is transmitted between different devices in the same network. Discuss the two principal functions of a...
Solve asap please 2 A mixture of ethylene and oxygen (67% C,H4 and 33% O2) exists at 25 atm and 3 o'C. Calculate: Partial fugacities of C2H4 and O2 using Lewis Randall Rule. ii) i) Activity of C,H4...
Prove that a diagonal matrix D = diag(d1,... , dn) is invertible if and only if all its diagonal entries are nonzero, in which case D-l = diag(1/d1..........1/dn) .
Two matrices A and B are said to be similar, written A ~ B, if there exists an invertible matrix S such that B = S-1 AS. Prove: (a) A ~ A (b) If A ~ B, then B ~ A. (c) If A ~ B ~ C, then A~ C.
How much must be deposited now at 5.25% interest to produce $300 at the end of ~very year for 10 years?
We want to electroplate all surfaces of a solid steel rod which is 300 mm long and 10 mm in diameter. We want a plating thickness of 1.00 mm. Our current is 20 Amps, and the plating material has a...
A steam of liquid water at 300 K Pa and 20 is mixed in an adiabatic (Q=0.0) mixing chamber with steam at 300 K Pa and 250 , which is entering at rate of 90 kg/s. The mixture is to leave as a...
What is the percentage increase in the theoretical power in wind when wind speed increases from 9 m/s to 10 m/s?
What is the future value of $3,617, given a discount rate of 8.6% and a time of 19 years?
A heating system that uses hot steam has a total heating load of 503 thousand btuh. How much heated Steam flow in pounds per hour ( lb/hr ) is required to satisfy the total load?
The condenser of a home refrigerator is commonly underneath the appliance; thus, the condensing refrigerant exchanges heat with household air, which has an average temperature of about 21C. It is...
What is a make-or-buy decision?
Suppose that is an eigenvalue of A. (a) Prove that c is an eigenvalue of the scalar multiple c A. (b) Prove that + d is an eigenvalue of A + d I. (c) More generally, c + d is an eigenvalue of B =...
Let A be a nonsingular square matrix. Prove the following formulas for its condition number: (a) (b) K(A) max{ || Au|| | || u || = 1} min{ || Au|| | ||u|| = 1)
Under the assumptions of Theorem 8.74, show that A B 2 is also minimized when B = A k among all matrices with rank B k. Theorem 8.74 Theorem 8.74 says that, in the latter cases, the number of...
State the dividend irrelevance proposition. What are the assumptions behind this proposition? Explain why this proposition does not hold in the real world. (20 marks)
How many monthly withdrawals of $1,400 will an investment of $75,000 sustain if the first withdrawal is made 12 months from now and the money earns 8.4% compounded monthly
1. You buy a bond with 3 years left to maturity and a yield to maturity of 6% for $920. After 1 year you receive a coupon payment of $30 and sell the bond for $940. What was your rate of return on...

Prove that if U is a nonsingular upper triangular matrix, then the diagonal entries of U-1 are

Question:

Step by Step Answer:

Since U 1 is also upper triangular the ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions