Question: If both A-1 and the LU factorization of an n n matrix A have already been computed, then it is more efficient to solve

If both A-1 and the LU factorization of an n × n matrix A have already been computed, then it is more efficient to solve a system Ax = b by multiplying A-1b rather than solving LUx = In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.
b using forward and back substitution.

Step by Step Solution

★★★★★

3.32 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The statement is false If A 1 and the LU factoriz... View full answer

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)

949-M-L-A-E (927).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

IT is changing the nature of accounting and the role of accountants. Write a two-page report describing what you think will be the nature and the value of accounting function in a large company in...

Suppose that A-1 and the LU factorization of A have already been determined. How many scalar additions and multiplications are necessary to compute A-1b? Compare this with the number of operations...

Compute the LU factorization of each of the following matrices. (a) (b) 4 2 113 246

Given the matrix (a) Compute the LU factorization of A. (b) Use the LU factorization to determine the value of det(A). 0 14 2 136 10 1234

Number 1 from pen and paper: Please solve the matlab portion. 1. Suppose you use the following MATLAB function to compute the LU decomposition of the matrix A defined in Pen-and-paper Problem 1....

I'm trying to write a code in matlab, such that it solves for a system Ay=b, where A is a square matrix of constant element values, b is a single column matrix of known values, and y is a single...

MAT 343 LAB 3 Example We can generate the three matrices listed in (1) using the following MATLAB commands >>E1eye (4) >> E1( [2,3], :) E1( [3,2], :) % swap rows 2 and 3 E1 = % generate the 4x4...

Matlab code please Problem 7 (10 points] Consider solving the linear system Ax = b, where A e Rnxn and beR. Suppose that we have computed a numerical solution x1 x. The residual is r = b Axi = AX -...

Please answer all parts and code preferably in Python. And provide explanation to every part of the question. Thanks 2.4. Write a routine for estimating the condition number of a matrix A. You may...

Please answer within 10hrs and I'll give u thumbs up. First pic is the question and the other pic is previous question and answer for your reference. thank you. Q4. From the previous questions, we...

All questions. 05:50:42 VA; 25% ' ASSIGNMENTNM1.pdf IQ 0+ Numerical Methods-Assignment-l Mathematical Prelimanaries, Taylor's Theorem, Order of Convergence (1) Let L be a real number and let {an} be...

What is the ideal work for the separation of an equimolar mixture of methane and ethane at 175C and 3 bar in a steady-flow process into product streams of the pure gases at 35C and 1 bar if Ta = 300...

Consider two very large parallel plates with diffuse, gray surfaces. Determine the irradiation and radiosity for the upper plate. What is the radiosity for the lower plate? What is the net radiation...

Including mobile phones in e - commerce:A . Does not require a new strategy.B . Is happening gradually.C . Has been a consolidated part of the market for at least twenty years.D . All of the above...

Beta Graphics, Inc., has the following data: Requirement 1. Perform a vertical analysis of Betas balance sheet for eachyear. BETA GRAPHICS, INC. Comparative Balance Sheet December 31, 2012 and 2011...

The Windshield People repair chips in car windshields in the companys home county. Rocky Chip, the owner, incurred the following operating costs for the month of February 2012: Salaries and wages . ....

Natalia Wallace is the new controller for Smart Software, Inc., which develops and sells education software. Shortly before the December 31 fiscal year-end, James Cauvet, the company president, asks...

What are some differences between financial and managerial accounting?

Figure gives the magnetization curve for a paramagnetic material. The vertical axis scale is set by a = 0.15, and the horizontal axis scale is set by b = 0.2 T/K. Let sam be the measured net...

Why are Right to Know laws important for employees and the community? What do these laws specifically address? What are the remedies for violation of these laws? How can communities and industry work...

In exercise 15 through 28, classify the quadric surface given by each equation and determine its standard form? 1. -x2 -y2 - z2 + 4xy + 4xz + 4yz = 3 2. 4x2 + 4y2 + 8z2 + 4xy - 4xz - 4yz + 6x - 10y +...

Find a column of the matrix in Exercise 39 that can be deleted and yet have the remaining matrix columns still span. R4 10 7 4 6 -8 4-6-10-3 7 -5-8 3 1 10 12 12

Find a column of the matrix in Exercise 40 that can be deleted and yet have the remaining matrix columns still span. Can you delete more than one column? R4 2937 7692 6467 1354 5713

Include the correct Excel Forumulas to solve this question

how to find the probability that 2-5 players ejected by hook during a given week x. P(x) 0 0.10 1 0.18 2 0.23 3 0.25 4 0.14 5 0.07 6 0.03 mean = 0.14285714 sd = 0.081998839

Read the question and answer the questions that follow: Determine the weighted average cost of capital using ( 1 ) book value weights; and ( 2 ) market value weights based on the following...