An alternative solution strategy, also called GaussJordan in some texts, is, once a pivot is in position, to use elementary row operations of type 1 to eliminate all entries both above and below it, thereby reducing the augmented matrix to diagonal form D c where D diag(d 1 , ,d n ) is a diagonal matrix containing the pivots The solutions x i c i d i are then obtained by simple division Is this strategy more efficient, less efficient, or the same as Gaussian Elimination with Back Substitution Justify your answer with an exact operations count

Question: An alternative solution strategy, also called GaussJordan in some texts, is, once a pivot is in position, to use elementary row operations of type #1

An alternative solution strategy, also called Gauss–Jordan in some texts, is, once a pivot is in position, to use elementary row operations of type #1 to eliminate all entries both above and below it, thereby reducing the augmented matrix to diagonal form D | c where D = diag(d₁, . . . ,d_n) is a diagonal matrix containing the pivots. The solutions x_i = c_i/d_i are then obtained by simple division. Is this strategy more efficient, less efficient, or the same as Gaussian Elimination with Back Substitution? Justify your answer with an exact operations count.

Step by Step Solution

★★★★★

3.33 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER The alternative solution strategy of GaussJordan eliminates the need for back substitution bu... 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

Students Have Also Explored These Related Applied Linear Algebra Questions!

List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...

Count the number of arithmetic operations needed to solve a system the "old-fashioned" way, by using elementary row operations of all three types, in the same order as the Gauss-Jordan scheme, to...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

Python code for part d Use stem import copy as CP def FirstNonZero_Index(R): #finds pivot for a row vector (R) m=-1 for n in range(len(R)): if R[n] != 0.0: m=n break return m #if the whole row is...

1. Describe the possible echelon forms of a nonzero 2 x 2 matrix. (3 Select all that apply. (Note that leading entries marked with a I may have any nonzero value and starred entries ( * ) may have...

1) Use the above function (you will need to add on to it) to solve for the following equations Ax=b in 50 unknowns, where A is a 50x50 matrix, b is a vector of size 50x1. Note that these are random...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

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...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Myriam works in the human resources department of a small legal and accounting firm. She meets with you to discuss the possibility of implementing a group disability benefits plan for her employees....

Discuss the reasons companies such as Under Armour or Calvin Klein might use an in-house agency rather than an external agency. Why might a company change from us9ng an in-house agency and hire an...

Suppose you take a long position in 6 crude oil futures contracts at a futures price of $ 4 5 pelbarrel. You want to hold your long position for one month, but you are worried that the crudeoil...

1. How are the net present value and profitability index of a project measured?

(a) Find three different permuted LU factorizations of the matrix (b) How many different permuted LU factorizations does A have? 213 101 011

What is the maximal number of permuted L U factorizations a regular 33 matrix can have? Give an example of such a matrix.

(a) Write a pseudocode program implementing the algorithm for finding the permuted LU factorization of a matrix. (b) Program your algorithm and test it on the examples in Exercise 1.4.19.

Which represented quadrilateral will be classified as strictly a kite? 11 a) (-1,2), (0, 0), (1, 1), (2, -1) b) (-3,0). (-2-3), (0, 1), (1, -2) c) (-3, 1), (-2, 2), (0, -2), (1,-1) d) (-1, -3), (0,...

We project unit sales for a new household-use laser-guided cockroach search and destroy system as follows: Unit Sales 99,000 111,000 134,000 140.000 93,000 The new system will be priced to sell at...

Co. Inc. buys on terms of 1/15, net 30 from its chief supplier. Suppose Co. Inc. doesn't take the discount and chooses to pay the supplier late. On average, Co. Inc. pays the supplier on the 35th day...