Prove that the determinant of a lower triangular matrix is the product of its diagonal entries.

Question:

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 08:29 AM

See More Questions

Prove that the determinant of a product is the product of the determinants |TS| = |T| |S| in this way. Fix the n n matrix S and consider the function d: Mnn R given by T |TS|/|S|. (a) Check that d...
Prove that the determinant of a matrix equals the determinant of its transpose using Laplace's expansion and induction on the size of the matrix.
Prove that the determinant of any triangular matrix, upper or lower, is the product down its diagonal.
TCP: the client sends only 1 message to the server hello from TCP Client and the server responds with the uppercase message. Update the program / make a simple chat program so that The client can...
The XYZ Company produces two products. The total profit achieved from these products is described by the following equation: Every 1,000 units of X1 requires one hour of time in the shipping...
Why might the cost of capital for a foreign project differ from that of an equivalent domestic project? Could it be lower? AppendixLO1
3.34 .006 d. Use a random number generator to randomly assign each of the 252 subjects to one of the three groups. Be sure to assign 84 subjects to each group.
The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following...
Exercise 12-14 Comparison of Projects Using Net Present Value (L012-2) in Labeau Products, Ltd., of Perth, Australia, has $25,000 to invest. The company is trying to decide between two alternative...
C11. A solid non-conducting disc of mass m and radius R has total charge Q is uniformly distributed on its surface. A light thin string is wound around the disc is connected to the light pulley P, as...
Prove that if A is a n x n matrix and c is a scalar, then det(c A) = cn det A.
Show that the set of complex numbers x + i y forms a real vector space under the operations of addition (x + iy) + (w + i v) = (x + u) + i (y + v) and scalar multiplication c(x + iy) = cx + i cy....
What requirement is imposed by the double-entry system in the recording of any business transaction? LO5
Home Base, Incorporated reports the following production cost information: Units produced 97,000 units Units sold 92,000 units Ending finished goods inventory 5,000 units Direct labor $17 per unit...
About New York City public sector finance. The other way is to delineate the problem. We should use data to show a problem, and then analyze the environment in which budgeting takes place to suggest,...
From a survey a company has determined that 23% of its customers are classified as "advocates" , 68% as "passives" and the remainder as "detractors" . Research suggests that during a year 15% of the...
The following are the transactions of Spotlighter, Incorporated, for the month of January. a. Borrowed $3,940 from a local bank on a note due in six months. b. Received $4,630 cash from investors and...
1. What are the deeper problems that plague in different forms it takes throughout the world according to the authors? Please, briefly explain. 2. Why was Joseph Schumpeter a pessimist about the...
Describe why bronze was one of the first alloys that humans used.
In 1995 Miguel purchased a home for $130,000. In 2000 he sold it for $170,000 and immediately purchased another one for $180,000, which he sold in 2007 for $235,000. How much taxable capital gain, if...
With A as in Exercise 18, find a nonzero vector in Nul A and a nonzero vector in Col A?
I can be shown that a solution of the system below is x1 = 3, x2 = 2, and x3 = - 1. Use this fact and the theory from this section to explain why another solution is x1 = 30, x2 = 20, and x3 = - 10,...
Consider the following two systems of equations: 5X1 + X2-3x3=0 9x1 + 2x2 + 5x3 = 1 4X1+ X2-6x3=9 5x1 + x2-3x3= 0 9x1 + 2x2 + 5x3 = 5 4X1 + X2-6x3=45
A local bookstore is considering adding a coffee shop to their store. Building the coffee shop will cost $256,340.00 today. The bookstore is going to try this project for five years. The bookstore...
What is the depreciation deduction, using each of the following methods, for the second year for an asset that costs $40,000 and has an estimated MV of $5,000 at the its seven-year useful life?...
How do we use the simulation analysis for financial decision making

Prove that the determinant of a lower triangular matrix is the product of its diagonal entries.

Question:

Step by Step Answer:

By Proposition 156 detL T detL If L is a l...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions