Question: Let A be a singular square matrix. Prove that there exist elementary matrices E1,... . EN such that A = E1 E2

Let A be a singular square matrix. Prove that there exist elementary matrices E1,... . EN such that A = E1 E2 ∙ ∙ ∙ En Z. where Z is a matrix with at least one all zero row.

Step by Step Solution

★★★★★

3.38 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

By Proposition 139 A can be reduced to row echelon form U by a ... 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)

952-M-L-A-E (1752).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be a nonsingular 2 Ã 2 matrix with singular value decomposition A = P QT and singular values Ï1 ¥ Ï2 > 0. (a) Prove that the image of the unit (Euclidean) circle under the...

(a) Prove that for any 2 Ã 2 matrix T there are scalars c0, . . . , c4 that are not all 0 such that the combination c4T4 + c3T3 + c2T2 + c1T + c0I is the zero matrix (where I is the 2 Ã...

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...

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...

FINAL Here is the nal. Try to adhere to conventions as much as possible. This will allow us to grade more accurately and eciently. Problem 5 covers material from this Wednesday up until next...

MATH 1300 D01/D02 Winter 2016 Assignment 4 SHOW ALL WORK to get full marks. Leave answers as exact answers. For example, leave it as fractions such as 1{7 as opposed to decimals such as 0.142857....

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:...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

You will notice that the cells in the utility table for you to complete include letters. Complete the cells with letter A through I and then indicate which location option is best. Weights: NPV = 0.7...

You have been given the task of assessing the financial performance of two separate companies operating in the retail industry. The financial information for these two companies is presented as...

If the international Fisher effect ( IFE ) holds, investors camot earn extra return by investing in foreign currencies with higher interest rate, in other wonds. the lowal inwestoes are eupected to...

The development team is building a new product for its company. This is a new product type at the company, and the market for the product is extremely unstable. According to the product manager, a...

Compute the products in Exercises 1-2 using (a) the definition, as in Example 1, and (b) the row-vector rule for computing Ax. If a product is undefined, explain why. 1. 2. 327

Given A and b in Exercises 1 and 2, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. 1. 2.

Repeat the requests from Exercise 15 with 1 -211 bi 01, and b=|b. b3 A=1-2 2 4-1

You want to create a portfolio equally as risky as the market, and you have $250,000 to invest. Given this information, fill in the three missing pieces of information in the following table. Show...

In the Loan sheet, insert formulas in the range E2:E4 to calculate the loan amount, the number of payment periods, and the monthly interest rate, respectively. Use cell references in all formulas. 13...

In Problems 26 through 28, given the following information on Hypothesis Test. 26) Dr. Dai claims that u * 173 cm and Sample data set X is (X1, X2, ....,X36) with >X= 6300 cm, 26) and sample standard...